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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 5, Pages 1116–1175 (Mi izv2003)  

This article is cited in 168 scientific papers (total in 168 papers)

Quantization

F. A. Berezin


Abstract: In this article we propose a general definition for the quantization of classical mechanics with an arbitrary phase space. We consider the case where the phase space is a complex Kählerian manifold. As an example we consider uniform bounded regions in $C^n$ with a Bergman metric, and also the two-dimensional cylinder and torus.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:5, 1109–1165

Bibliographic databases:

UDC: 513.88
MSC: Primary 70H15, 81A17; Secondary 81-02, 70G99
Received: 06.09.1973

Citation: F. A. Berezin, “Quantization”, Izv. Akad. Nauk SSSR Ser. Mat., 38:5 (1974), 1116–1175; Math. USSR-Izv., 8:5 (1974), 1109–1165

Citation in format AMSBIB
\Bibitem{Ber74}
\by F.~A.~Berezin
\paper Quantization
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 5
\pages 1116--1175
\mathnet{http://mi.mathnet.ru/izv2003}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=395610}
\zmath{https://zbmath.org/?q=an:0312.53049}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 5
\pages 1109--1165
\crossref{https://doi.org/10.1070/IM1974v008n05ABEH002140}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. A. Berezin, “Quantization in complex symmetric spaces”, Math. USSR-Izv., 9:2 (1975), 341–379  mathnet  crossref  mathscinet  zmath
    2. Yu. M. Shirokov, “Different quantizations and different classical limits of quantum theory”, Theoret. and Math. Phys., 29:3 (1976), 1091–1100  mathnet  crossref  mathscinet
    3. Yu. M. Shirokov, “Combined algebra for quantum and classical mechanics”, Theoret. and Math. Phys., 28:3 (1976), 806–813  mathnet  crossref  mathscinet  zmath
    4. A. A. Kirillov, “Local Lie algebras”, Russian Math. Surveys, 31:4 (1976), 55–75  mathnet  crossref  mathscinet  zmath
    5. R. S. Ismagilov, “On unitary representations of the group $C_0^\infty(X, G)$, $G=SU_2$”, Math. USSR-Sb., 29:1 (1976), 105–117  mathnet  crossref  mathscinet  zmath  isi
    6. Yu. M. Shirokov, “Perturbation theory with respect to Planck's constant”, Theoret. and Math. Phys., 31:3 (1977), 488–492  mathnet  crossref
    7. M. A. Antonets, “Classical limit of Weyl quantization”, Theoret. and Math. Phys., 38:3 (1979), 219–228  mathnet  crossref  mathscinet
    8. I. A. Shereshevskij, “Quantization and commutative superalgebras”, Lett Math Phys, 5:5 (1981), 429  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. M. A. Antonets, I. A. Shereshevskii, “Weyl quantization on compact Abelian groups and the quantum mechanics of almost periodic systems”, Theoret. and Math. Phys., 48:1 (1981), 597–604  mathnet  crossref  mathscinet  zmath  isi
    10. V. P. Maslov, V. E. Nazaikinskii, “Asymptotics for equations with singularities in the characteristics”, Math. USSR-Izv., 19:2 (1982), 315–347  mathnet  crossref  mathscinet  zmath
    11. Carlos Moreno, Pilar Ortega-Navarro, “*-Products on D 1 (ℂ), S 2 and related spectral analysis”, Lett Math Phys, 7:3 (1983), 181  crossref  mathscinet  zmath  isi
    12. Victor Guillemin, “Toeplitz operators in n-dimensions”, Integr equ oper theory, 7:2 (1984), 145  crossref  mathscinet  zmath
    13. M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. G. K. Tolokonnikov, “Algebras of observables of nearly canonical physical theories. II”, Theoret. and Math. Phys., 61:2 (1984), 1072–1077  mathnet  crossref  mathscinet  isi
    15. Alejandro Uribe, “A symbol calculus for a class of pseudodifferential operators on Sn and band asymptotics”, Journal of Functional Analysis, 59:3 (1984), 535  crossref
    16. Carlos Moreno, “Geodesic symmetries and invariant star products on Kähler symmetric spaces”, Lett Math Phys, 13:3 (1987), 245  crossref  mathscinet  zmath  isi
    17. G. M. Tuynman, “Quantization: Towards a comparison between methods”, J Math Phys (N Y ), 28:12 (1987), 2829  crossref  mathscinet  zmath  adsnasa
    18. Andre Unterberger, Julianne Unterberger, “A quantization of the cartan domain BD I (q = 2) and operators on the light cone”, Journal of Functional Analysis, 72:2 (1987), 279  crossref
    19. David Gurarie, “Zonal Schrödinger operators on then-sphere: Inverse spectral problem and rigidity”, Comm Math Phys, 131:3 (1990), 571  crossref  mathscinet  zmath
    20. J. Rawnsley, M. Cahen, S. Gutt, “Quantization of Kähler manifolds I: geometric interpretation of Berezin's quantization”, Journal of Geometry and Physics, 7:1 (1990), 45  crossref
    21. Martin Bordemann, Jens Hoppe, Peter Schaller, Martin Schlichenmaier, “gl(∞) and geometric quantization”, Comm Math Phys, 138:2 (1991), 209  crossref  mathscinet  zmath
    22. Roberto Floreanini, Roberto Percacci, Ergin Sezgin, “Infinite dimensional algebras in Chern–Simons quantum mechanics”, Physics Letters B, 261:1-2 (1991), 51  crossref
    23. L. A. Coburn, “Deformation estimates for the Berezin-Toeplitz quantization”, Comm Math Phys, 149:2 (1992), 415  crossref  mathscinet  zmath  adsnasa
    24. Miroslav Engliš, “Density of algebras generated by Toeplitz operators on Bergman spaces”, Ark Mat, 30:1-2 (1992), 227  crossref  mathscinet  zmath  isi
    25. A. Vourdas, “Coherent states on the m-sheeted covering group of SU(1,1)”, J Math Phys (N Y ), 34:3 (1993), 1223  crossref  mathscinet  zmath  adsnasa
    26. David Borthwick, Slawomir Klimek, Andrzej Lesniewski, Maurizio Rinaldi, “Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds”, Comm Math Phys, 153:1 (1993), 49  crossref  mathscinet  zmath
    27. D Bar-Moshe, M S Marinov, J Phys A Math Gen, 27:18 (1994), 6287  crossref  mathscinet  zmath  adsnasa
    28. A. Vourdas, “Coherent states on the m-sheeted complex plane”, J Math Phys (N Y ), 35:5 (1994), 2687  crossref  mathscinet  zmath  adsnasa
    29. A. Vourdas, “Thermal coherent states in the Bargmann representation”, Phys Rev A, 50:4 (1994), 3331  crossref  mathscinet  adsnasa  isi
    30. Martin Bordemann, Eckhard Meinrenken, Martin Schlichenmaier, “Toeplitz quantization of Kähler manifolds anggl(N), N→∞ limits”, Comm Math Phys, 165:2 (1994), 281  crossref  mathscinet  zmath
    31. A. Unterberger, H. Upmeier, “The Berezin transform and invariant differential operators”, Comm Math Phys, 164:3 (1994), 563  crossref  mathscinet  zmath  adsnasa
    32. M. V. Karasev, M. B. Kozlov, “Representations of Compact Semisimple Lie Algebras over Lagrangian Submanifolds”, Funct. Anal. Appl., 28:4 (1994), 238–246  mathnet  crossref  mathscinet  zmath  isi
    33. Wojciech Mulak, “Quantum SU(2,2)-harmonic oscillator”, Reports on Mathematical Physics, 34:2 (1994), 143  crossref
    34. Pierre Cartier, Cécile DeWitt-Morette, “A new perspective on functional integration”, J Math Phys (N Y ), 36:5 (1995), 2237  crossref  mathscinet  zmath
    35. A. Vourdas, “SU(2) coherent states on an m-sheeted covering of the sphere”, J Math Phys (N Y ), 36:9 (1995), 4757  crossref  mathscinet  zmath  adsnasa
    36. A. Vourdas, “Displaced negative-binomial mixed states: Generalized thermo-field-dynamics”, Phys Rev A, 51:3 (1995), 2353  crossref  adsnasa  isi
    37. M. S. Marinov, “Path integrals on homogeneous manifolds”, J Math Phys (N Y ), 36:5 (1995), 2458  crossref  mathscinet  zmath  adsnasa
    38. S. S. Akbarov, “Differential geometry and quantization on a locally compact group”, Izv. Math., 59:2 (1995), 271–286  mathnet  crossref  mathscinet  zmath  isi
    39. Marco Matone, “The Higgs model for anyons and Liouville action”, Journal of Geometry and Physics, 17:1 (1995), 49  crossref
    40. A. Vourdas, “Dirac's contour representation in thermofield dynamics”, Phys Rev A, 53:3 (1996), R1205  crossref  mathscinet  adsnasa  isi
    41. Alexander V. Karabegov, “Deformation quantizations with separation of variables on a Kähler manifold”, Comm Math Phys, 180:3 (1996), 745  crossref  mathscinet  zmath  elib
    42. Vladimir V. Kisil, Enrique Ramírez de Arellano, “The Riesz-Clifford Functional Calculus for Non-Commuting Operators and Quantum Field Theory”, Math Meth Appl Sci, 19:8 (1996), 593  crossref  mathscinet  zmath
    43. André Unterberger, Julianne Unterberger, “Algebras of symbols and modular forms”, J Anal Math, 68:1 (1996), 121  crossref  mathscinet  zmath  isi
    44. A. V. Karabegov, “On the Deformation Quantization, on a Kähler Manifold, Associated with a Berezin Quantization”, Funct. Anal. Appl., 30:2 (1996), 142–144  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    45. M. Bordemann, M. Brischle, C. Emmrich, S. Waldmann, “Subalgebras with converging star products in deformation quantization: An algebraic construction for CPn”, J. Math. Phys, 37:12 (1996), 6311  crossref
    46. J. Gratus, “A natural basis of states for the noncommutative sphere and its Moyal bracket”, J Math Phys (N Y ), 38:8 (1997), 4283  crossref  mathscinet  zmath  adsnasa
    47. Oleg V. Prezhdo, “Mixing quantum and classical mechanics”, Phys Rev A, 56:1 (1997), 162  crossref  mathscinet  isi
    48. J A de Azcárraga, J M Izquierdo, J C Pérez Bueno, J Phys A Math Gen, 30:18 (1997), L607  crossref  zmath
    49. Ursula Carow-Watamura, Satoshi Watamura, “Chirality and Dirac operator on noncommutative sphere”, Comm Math Phys, 183:2 (1997), 365  crossref  mathscinet  zmath
    50. D. Bowes, K.C. Hannabuss, “Weyl quantization and star products”, Journal of Geometry and Physics, 22:4 (1997), 319  crossref
    51. Stefan Berceanu, “A remark on Berezin's quantization and cut locus”, Reports on Mathematical Physics, 40:2 (1997), 159  crossref
    52. E A Kochetov, J Phys A Math Gen, 31:19 (1998), 4473  crossref  mathscinet  zmath  adsnasa
    53. A Vourdas, R F Bishop, J Phys A Math Gen, 31:42 (1998), 8563  crossref  mathscinet  zmath  adsnasa
    54. A. V. Karabegov, “Strict Deformation Quantization on a Pseudo-Kähler Orbit of a Compact Lie Group”, Funct. Anal. Appl., 32:1 (1998), 51–53  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    55. S. Chountasis, A. Vourdas, “Weyl and Wigner functions in an extended phase-space formalism”, Phys Rev A, 58:3 (1998), 1794  crossref  isi
    56. S. Chountasis, A. Vourdas, “Weyl functions and their use in the study of quantum interference”, Phys Rev A, 58:2 (1998), 848  crossref  isi
    57. Miroslav Engliš, “Invariant Operators and the Berezin Transform on Cartan Domains”, Math Nachr, 195:1 (1998), 61  crossref
    58. M Karasev, “Advances in quantization: quantum tensors, explicit star-products, and restriction to irreducible leaves”, Differential Geometry and its Applications, 9:1-2 (1998), 89  crossref  elib
    59. G. van Dijk, V.F. Molchanov, “The Berezin form for rank one para-Hermitian symmetric spaces”, Journal de Mathématiques Pures et Appliquées, 77:8 (1998), 747  crossref  elib
    60. S. Groot Nibbelink, J.W. van Holten, “Matter coupling and anomaly cancellation in supersymmetric σ-models”, Physics Letters B, 442:1-4 (1998), 185  crossref
    61. URSULA CAROW-WATAMURA, SATOSHI WATAMURA, “DIFFERENTIAL CALCULUS ON FUZZY SPHERE AND SCALAR FIELD”, Int. J. Mod. Phys. A, 13:19 (1998), 3235  crossref
    62. S Chountasis, A Vourdas, J Phys A Math Gen, 32:40 (1999), 6949  crossref  mathscinet  zmath  adsnasa
    63. Bernhard Bodmann, Hajo Leschke, Simone Warzel, “A rigorous path integral for quantum spin using flat-space Wiener regularization”, J Math Phys (N Y ), 40:6 (1999), 2549  crossref  mathscinet  zmath  adsnasa
    64. G. Van Dijk, V.F. Molchanov, “Tensor products of maximal degenerate series representations of the group SL(n, R)”, Journal de Mathématiques Pures et Appliquées, 78:1 (1999), 99  crossref  elib
    65. Vladimir V. Kisil, “Relative Convolutions”, Advances in Mathematics, 147:1 (1999), 35  crossref
    66. M. Karasev, E. Novikova, “Coherent transform of the spectral problem and algebras with nonlinear commutation relations”, J Math Sci, 95:6 (1999), 2703  crossref
    67. G W Gibbons, Class Quantum Grav, 17:5 (2000), 1071  crossref  mathscinet  zmath  adsnasa
    68. E. Fricain, “Uniqueness theorems for analytic vector-valued functions”, Journal of Mathematical Sciences (New York), 101:3 (2000), 3193  crossref  mathscinet
    69. Miroslav Engli, “The asymptotics of a Laplace integral on a Kähler manifold”, crll, 2000:528 (2000), 1  crossref  mathscinet
    70. Miroslav Engliš, “A Forelli–Rudin Construction and Asymptotics of Weighted Bergman Kernels”, Journal of Functional Analysis, 177:2 (2000), 257  crossref
    71. Michael Penkava, Pol Vanhaecke, “Deformation Quantization of Polynomial Poisson Algebras”, Journal of Algebra, 227:1 (2000), 365  crossref
    72. Stefan Berceanu, Martin Schlichenmaier, “Coherent state embeddings, polar divisors and Cauchy formulas”, Journal of Geometry and Physics, 34:3-4 (2000), 336  crossref
    73. C C Chong, A Vourdas, J Phys A Math Gen, 34:46 (2001), 9849  crossref  mathscinet  zmath  adsnasa
    74. E. Strahov, “Berry’s phase for compact Lie groups”, J Math Phys (N Y ), 42:5 (2001), 2008  crossref  mathscinet  zmath  adsnasa
    75. Osman Teoman Turgut, “Geometric quantization on the super-disk”, J Math Phys (N Y ), 42:9 (2001), 4258  crossref  mathscinet  zmath
    76. D. A. Leites, I. M. Shchepochkina, “How to Quantize the Antibracket”, Theoret. and Math. Phys., 126:3 (2001), 281–306  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    77. I. A. Batalin, M. A. Grigoriev, S. L. Lyakhovich, “Star Product for Second-Class Constraint Systems from a BRST Theory”, Theoret. and Math. Phys., 128:3 (2001), 1109–1139  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    78. Takaaki Nomura, “Berezin transforms and Laplace–Beltrami operators on homogeneous Siegel domains”, Differential Geometry and its Applications, 15:1 (2001), 91  crossref
    79. E. A. Kochetov, “Geometric derivation of nonlinear sigma model for the 1D antiferromagnet”, Phys. Atom. Nuclei, 64:12 (2001), 2195  crossref
    80. T A Osborn, M F Kondratieva, “Heisenberg evolution WKB and symplectic area phases”, J Phys A Math Gen, 35:25 (2002), 5279  crossref  mathscinet  zmath  adsnasa  elib
    81. M. V. Karasev, T. A. Osborn, “Symplectic areas, quantization, and dynamics in electromagnetic fields”, J Math Phys (N Y ), 43:2 (2002), 756  crossref  mathscinet  zmath  adsnasa  elib
    82. M. V. Karasev, E. M. Novikova, “Nonlinear Commutation Relations: Representations by Point-Supported Operators”, Math. Notes, 72:1 (2002), 48–65  mathnet  crossref  crossref  mathscinet  zmath  isi
    83. M. T. Karaev, “Berezin Symbols and Schatten–von Neumann Classes”, Math. Notes, 72:2 (2002), 185–192  mathnet  crossref  crossref  mathscinet  zmath  isi
    84. A J Bracken, G Cassinelli, J G Wood, “Quantum symmetries and the Weyl Wigner product of group representations”, J Phys A Math Gen, 36:4 (2003), 1033  crossref  mathscinet  zmath  adsnasa  elib
    85. Alfredo M Ozorio de Almeida, “Decoherence of semiclassical Wigner functions”, J Phys A Math Gen, 36:1 (2003), 67  crossref  mathscinet  zmath  elib
    86. A Vourdas, “Factorization in finite quantum systems”, J Phys A Math Gen, 36:20 (2003), 5645  crossref  mathscinet  zmath  adsnasa  elib
    87. Nikolai Neumaier, Stefan Waldmann, “Morita equivalence bimodules for Wick type star products”, Journal of Geometry and Physics, 47:2-3 (2003), 177  crossref
    88. Bernhard G. Bodmann, “Construction of self-adjoint Berezin–Toeplitz operators on Kähler manifolds and a probabilistic representation of the associated semigroups”, Journal of Geometry and Physics, 47:2-3 (2003), 128  crossref
    89. Claudio Arezzo, Andrea Loi, “Quantization of Kähler manifolds and the asymptotic expansion of Tian–Yau–Zelditch”, Journal of Geometry and Physics, 47:1 (2003), 87  crossref
    90. Erik Guentner, “Berezin Quantization and K-Homology”, Commun. Math. Phys, 240:3 (2003), 423  crossref
    91. Mikhail Pletyukhov, “On the extra phase correction to the semiclassical spin coherent-state propagator”, J Math Phys (N Y ), 45:5 (2004), 1859  crossref  mathscinet  zmath  isi  elib
    92. A. Vourdas, “Local correlations and uncertainties in one-mode systems”, Phys Rev A, 69:2 (2004), 022108  crossref  mathscinet  adsnasa  isi
    93. M V Karasev, T A Osborn, “Quantum magnetic algebra and magnetic curvature”, J Phys A Math Gen, 37:6 (2004), 2345  crossref  mathscinet  zmath  adsnasa  isi  elib
    94. ANDREA LOI, “THE TIAN–YAU–ZELDITCH ASYMPTOTIC EXPANSION FOR REAL ANALYTIC KÄHLER METRICS”, Int. J. Geom. Methods Mod. Phys, 01:03 (2004), 253  crossref
    95. Martin Schlichenmaier, “Deformation quantization for almost-K¨ahler manifolds”, Journal of Nonlinear Mathematical Physics, 11:sup1 (2004), 49  crossref
    96. B.G.. Bodmann, “A Lower Bound for the Wehrl Entropy of Quantum Spin with Sharp High-Spin Asymptotics”, Commun. Math. Phys, 250:2 (2004), 287  crossref
    97. M V Karasev, T A Osborn, “Cotangent bundle quantization: entangling of metric and magnetic field”, J Phys A Math Gen, 38:40 (2005), 8549  crossref  mathscinet  zmath  adsnasa  isi  elib
    98. C. Lei, A. Vourdas, A. Wünsche, “Analytic and contour representations in the unit disk based on SU(1,1) coherent states”, J Math Phys (N Y ), 46:11 (2005), 112101  crossref  mathscinet  zmath  adsnasa  isi
    99. Benjamin Cahen, “Contractions ofSU(1, n) andSU(n+1) via Berezin quantization”, J Anal Math, 97:1 (2005), 83  crossref  mathscinet  isi
    100. O. N. Grigor'ev, M. V. Karasev, “Dynamical equations for the quantum product on a symplectic space in affine coordinates”, Math. Notes, 77:1 (2005), 39–47  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    101. Jacques Faraut, Michael Pevzner, “Berezin kernels and analysis on Makarevich spaces”, Indagationes Mathematicae, 16:3-4 (2005), 461  crossref  elib
    102. V.I. Man'ko, G. Marmo, P. Vitale, “Phase space distributions and a duality symmetry for star products”, Physics Letters A, 334:1 (2005), 1  crossref  elib
    103. Keiji Izuchi, Kou Hei Izuchi, “Polynomials having leading terms over in the Fock space”, Journal of Functional Analysis, 225:2 (2005), 439  crossref
    104. Andrea Loi, “A Laplace integral on a Kähler manifold and Calabi's diastasis function”, Differential Geometry and its Applications, 23:1 (2005), 55  crossref
    105. Andrea Loi, “Regular quantizations of Kähler manifolds and constant scalar curvature metrics”, Journal of Geometry and Physics, 53:3 (2005), 354  crossref
    106. STEFAN WALDMANN, “STATES AND REPRESENTATIONS IN DEFORMATION QUANTIZATION”, Rev. Math. Phys, 17:01 (2005), 15  crossref
    107. S. TWAREQUE ALI, MIROSLAV ENGLIŠ, “QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS”, Rev. Math. Phys, 17:04 (2005), 391  crossref
    108. A Vourdas, “Analytic representations in quantum mechanics”, J Phys A Math Gen, 39:7 (2006), R65  crossref  mathscinet  zmath  adsnasa  isi
    109. M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, Journal of Mathematical Sciences, 151:6 (2008), 3473–3496  mathnet  crossref  zmath  elib
    110. A. M. Vershik, M. I. Graev, “Structure of the complementary series and special representations of the groups $O(n,1)$ and $U(n,1)$”, Russian Math. Surveys, 61:5 (2006), 799–884  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    111. J. Math. Sci. (N. Y.), 141:4 (2007), 1494–1505  mathnet  crossref  mathscinet  zmath  elib
    112. Mubariz T. Karaev, “Berezin symbol and invertibility of operators on the functional Hilbert spaces”, Journal of Functional Analysis, 238:1 (2006), 181  crossref
    113. Zoran Škoda, “Coherent States for Hopf Algebras”, Lett Math Phys, 81:1 (2007), 1  crossref  mathscinet  zmath  isi
    114. Sergiu I. Vacaru, “Deformation quantization of almost Kähler models and Lagrange-Finsler spaces”, J Math Phys (N Y ), 48:12 (2007), 123509  crossref  mathscinet  zmath  isi  elib
    115. Alexander V. Karabegov, “A Formal Model of Berezin-Toeplitz Quantization”, Comm Math Phys, 274:3 (2007), 659  crossref  mathscinet  zmath  isi  elib
    116. Victor P. Palamodov, “Associative Deformations of Complex Analytic Spaces”, Lett Math Phys, 82:2-3 (2007), 191  crossref  mathscinet  zmath  isi
    117. Yan V Fyodorov, Boris A Khoruzhenko, “A few remarks on colour–flavour transformations, truncations of random unitary matrices, Berezin reproducing kernels and Selberg-type integrals”, J Phys A Math Theor, 40:4 (2007), 669  crossref  mathscinet  zmath  isi
    118. Donara Nguon, “Covariant symbolic calculus for Toeplitz operators on the sphere”, Integral Transforms and Special Functions, 18:4 (2007), 255  crossref  elib
    119. Olga V. Man'ko, Vladimir I. Man'ko, Giuseppe Marmo, Patrizia Vitale, “Star products, duality and double Lie algebras”, Physics Letters A, 360:4-5 (2007), 522  crossref  elib
    120. William D. Kirwin, “Coherent states in geometric quantization”, Journal of Geometry and Physics, 57:2 (2007), 531  crossref
    121. Pierre Bieliavsky, Charles Jego, Jan Troost, “Open strings in Lie groups and associative products”, Nuclear Physics B, 782:1-2 (2007), 94  crossref
    122. P. O. Kazinski, “Stochastic deformation of a thermodynamic symplectic structure”, Phys Rev E, 79:1 (2009), 011105  crossref  adsnasa  isi
    123. T A Osborn, Karl-Peter Marzlin, “Moyal phase-space analysis of nonlinear optical Kerr media”, J Phys A Math Theor, 42:41 (2009), 415302  crossref  isi  elib
    124. David Bar-Moshe, “A Method for Weight Multiplicity Computation Based on Berezin Quantization”, SIGMA, 5 (2009), 091, 12 pp.  mathnet  crossref  mathscinet
    125. Klaus Bering, “Three Natural Generalizations of Fedosov Quantization”, SIGMA, 5 (2009), 036, 21 pp.  mathnet  crossref  mathscinet  zmath
    126. Miroslav Englis, Harald Upmeier, “Toeplitz Quantization and Asymptotic Expansions: Geometric Construction”, SIGMA, 5 (2009), 021, 30 pp.  mathnet  crossref  mathscinet  zmath
    127. Molchanov V.F., “Kvantovanie na para-ermitovykh simmetricheskikh prostranstvakh”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 14:6-3 (2009), 1426–1442  elib
    128. P. Aniello, A. Ibort, V.I. Man'ko, G. Marmo, “Remarks on the star product of functions on finite and compact groups”, Physics Letters A, 373:4 (2009), 401  crossref  elib
    129. Kamthorn Chailuek, Brian C. Hall, “Toeplitz Operators on Generalized Bergman Spaces”, Integr equ oper theory, 2010  crossref  isi
    130. Miroslav Engliš, Harald Upmeier, “Toeplitz quantization and asymptotic expansions for real bounded symmetric domains”, Math Z, 2010  crossref
    131. Johannes Löffler, “Fedosov differentials and Catalan numbers”, J Phys A Math Theor, 43:23 (2010), 235404  crossref
    132. Miroslav Engliš, Harald Upmeier, “Toeplitz Quantization and Asymptotic Expansions: Peter–Weyl Decomposition”, Integr equ oper theory, 2010  crossref
    133. J A de Azcárraga, J M Izquierdo, “$n$-ary algebras: a review with applications”, J Phys A Math Theor, 43:29 (2010), 293001  crossref
    134. Benjamin Cahen, “Stratonovich-Weyl correspondence for compact semisimple Lie groups”, Rend Circ Mat Palermo, 59:3 (2010), 331  crossref
    135. M. T. Karaev, M. Zeltser, “On Abel Convergence of Double Sequences”, Num. Functional Analysis & Optimization, 31:10 (2010), 1185  crossref
    136. W. Bauer, L.A. Coburn, J. Isralowitz, “Heat flow, BMO, and the compactness of Toeplitz operators”, Journal of Functional Analysis, 259:1 (2010), 57  crossref
    137. Miroslav Engliš, “Berezin transform on the harmonic Fock space”, Journal of Mathematical Analysis and Applications, 367:1 (2010), 75  crossref
    138. Mübariz Tapd{\i}goǧlu Karaev, “(e)-convergence and related problem”, Comptes Rendus Mathematique, 348:19-20 (2010), 1059  crossref
    139. Nicolae Cotfas, Jean Pierre Gazeau, Apostol Vourdas, “Finite-dimensional Hilbert space and frame quantization”, J. Phys. A: Math. Theor, 44:17 (2011), 175303  crossref
    140. P. Watson, A. Bracken, “Phase-space spinor amplitudes for spin-1/2 systems”, Phys. Rev. A, 83:4 (2011)  crossref
    141. Benjamin Cahen, “Berezin quantization for holomorphic discrete series representations: the non-scalar case”, Beitr Algebra Geom, 2011  crossref
    142. Bo Li, Yifei Pan, “Berezin's operator calculus and higher order Schwarz–Pick lemma”, Complex Variables and Elliptic Equations, 2011, 1  crossref
    143. Maciej Błaszak, Ziemowit Domański, “Phase space quantum mechanics”, Annals of Physics, 2011  crossref
    144. Zouhaïr Mouayn, “Coherent States Quantization for Generalized Bargmann Spaces with Formulae for Their Attached Berezin Transforms in Terms of the Laplacian on ℂ N”, J Fourier Anal Appl, 2011  crossref
    145. Gorshkov A.S., Makarov A.G., Rymkevich P.P., “Fiziko-matematicheskie osnovy dlya opisaniya nestatsionarnoi teploprovodnosti cherez mnogosloinye izdeliya tekstilnoi i shveinoi promyshlennosti v dinamicheskom rezhime ekspluatatsii”, Izvestiya vysshikh uchebnykh zavedenii. Tekhnologiya legkoi promyshlennosti, 13:3 (2011), 33–36  elib
    146. Andrea Loi, Roberto Mossa, “Berezin quantization of homogeneous bounded domains”, Geom Dedicata, 2012  crossref
    147. Hao Xu, “An Explicit Formula for the Berezin Star Product”, Lett Math Phys, 2012  crossref
    148. M. T. Karaev, “Reproducing Kernels and Berezin Symbols Techniques in Various Questions of Operator Theory”, Complex Anal. Oper. Theory, 2012  crossref
    149. G. Amosov, Ya. Korennoy, V. Man'ko, “Description and measurement of observables in the optical tomographic probability representation of quantum mechanics”, Phys. Rev. A, 85:5 (2012)  crossref
    150. Hao Xu, “A Closed Formula for the Asymptotic Expansion of the Bergman Kernel”, Commun. Math. Phys, 2012  crossref
    151. A. Rabeie, “Quantum physics of an elementary system in de Sitter space”, Eur. Phys. J. C, 72:9 (2012)  crossref
    152. S. A. A. GHORASHI, R. ROKNIZADEH, M. BAGHERI HAROUNI, “GENERALIZED COHERENT STATES APPROACH TO DEFORMATION QUANTIZATION”, Int. J. Mod. Phys. A, 27:18 (2012), 1250095  crossref
    153. Hao Xu, “On a Graph Theoretic Formula of Gammelgaard for Berezin–Toeplitz Quantization”, Lett Math Phys, 2012  crossref
    154. Zorin A.V., “Operatsionnaya model kvantovykh izmerenii kuryshkina-vudkevicha”, Vestnik Rossiiskogo universiteta druzhby narodov. Seriya: Matematika, informatika, fizika, 2012, no. 2, 43–55  elib
    155. Mubariz T. Karaev, “Tauberian-type theorem for (e)-convergent sequences”, Comptes Rendus Mathematique, 2013  crossref
    156. Petr Blaschke, “Berezin transform on Harmonic Bergman spaces on the real Ball”, Journal of Mathematical Analysis and Applications, 2013  crossref
    157. Donara Nguon, “Bessel integral operators”, Integral Transforms and Special Functions, 2014, 1  crossref
    158. S. Twareque Ali, Miroslav Engliš, “Hermite polynomials and quasi-classical asymptotics”, J. Math. Phys, 55:4 (2014), 042102  crossref
    159. Zhiming Feng, Zhenhan Tu, “Balanced metrics on some Hartogs type domains over bounded symmetric domains”, Ann Glob Anal Geom, 2014  crossref
    160. Benjamin Cahen, “Coherent states and Berezin quantization for non-scalar holomorphic representations”, Ricerche mat, 2015  crossref
    161. Andrea Loi, Michela Zedda, “On the coefficients of TYZ expansion of locally Hermitian symmetric spaces”, manuscripta math, 2015  crossref
    162. R. Roknizadeh, H. Heydari, “Complexifier Method for Generation of Coherent States of Nonlinear Harmonic Oscillator”, Found Phys, 2015  crossref
    163. Petr Blaschke, Jiří Jahn, “Berezin transform of two arguments”, Journal of Functional Analysis, 2015  crossref
    164. Karl-Peter Marzlin, Stephen Deering, “The Moyal equation for open quantum systems”, J. Phys. A: Math. Theor, 48:20 (2015), 205301  crossref
    165. Miroslav Engliš, S. Twareque Ali, “Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics”, J. Math. Phys, 56:7 (2015), 072109  crossref
    166. F. Rădulescu, “Endomorphisms of spaces of virtual vectors fixed by a discrete group”, Russian Math. Surveys, 71:2 (2016), 291–343  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    167. Stefan Berceanu, “Balanced Metric and Berezin Quantization on the Siegel–Jacobi Ball”, SIGMA, 12 (2016), 064, 28 pp.  mathnet  crossref
    168. Stefan Berceanu, “The Real Jacobi Group Revisited”, SIGMA, 15 (2019), 096, 50 pp.  mathnet  crossref
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