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Funktsional. Anal. i Prilozhen., 1976, Volume 10, Issue 4, Pages 13–29 (Mi faa2188)  

This article is cited in 40 scientific papers (total in 41 papers)

Fractional powers of operators and Hamiltonian systems

I. M. Gel'fand, L. A. Dikii

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English version:
Functional Analysis and Its Applications, 1976, 10:4, 259–273

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Received: 22.06.1976

Citation: I. M. Gel'fand, L. A. Dikii, “Fractional powers of operators and Hamiltonian systems”, Funktsional. Anal. i Prilozhen., 10:4 (1976), 13–29; Funct. Anal. Appl., 10:4 (1976), 259–273

Citation in format AMSBIB
\by I.~M.~Gel'fand, L.~A.~Dikii
\paper Fractional powers of operators and Hamiltonian systems
\jour Funktsional. Anal. i Prilozhen.
\yr 1976
\vol 10
\issue 4
\pages 13--29
\jour Funct. Anal. Appl.
\yr 1976
\vol 10
\issue 4
\pages 259--273

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    This publication is cited in the following articles:
    1. A. M. Vinogradov, B. A. Kupershmidt, “The structures of Hamiltonian mechanics”, Russian Math. Surveys, 32:4 (1977), 177–243  mathnet  crossref  mathscinet  zmath
    2. I. M. Krichever, “Methods of algebraic geometry in the theory of non-linear equations”, Russian Math. Surveys, 32:6 (1977), 185–213  mathnet  crossref  mathscinet  zmath
    3. I. M. Krichever, “Integration of nonlinear equations by the methods of algebraic geometry”, Funct. Anal. Appl., 11:1 (1977), 12–26  mathnet  crossref  mathscinet  zmath
    4. I. M. Gel'fand, L. A. Dikii, “The resolvent and Hamiltonian systems”, Funct. Anal. Appl., 11:2 (1977), 93–105  mathnet  crossref  mathscinet  zmath
    5. I. M. Gel'fand, L. A. Dikii, “The calculus of jets and nonlinear Hamiltonian systems”, Funct. Anal. Appl., 12:2 (1978), 81–94  mathnet  crossref  mathscinet  zmath
    6. Yu. I. Manin, “Matrix solitons and bundles over curves with singularities”, Funct. Anal. Appl., 12:4 (1978), 286–295  mathnet  crossref  mathscinet  zmath
    7. A. P. Veselov, “Hamiltonian formalism for the Novikov–Krichever equations for the commutativity of two operators”, Funct. Anal. Appl., 13:1 (1979), 1–6  mathnet  crossref  mathscinet  zmath
    8. I. M. Gel'fand, I. Ya. Dorfman, “Hamiltonian operators and algebraic structures related to them”, Funct. Anal. Appl., 13:4 (1979), 248–262  mathnet  crossref  mathscinet  zmath
    9. D. R. Lebedev, Yu. I. Manin, “Gel'fand–Dikii Hamiltonian operator and the coadjoint representation of the volterra group”, Funct. Anal. Appl., 13:4 (1979), 268–273  mathnet  crossref  mathscinet  zmath
    10. F. A. Berezin, A. M. Perelomov, “Group theoretic interpretation of equations of Korteweg - de Vries type”, Funct. Anal. Appl., 14:2 (1980), 119–121  mathnet  crossref  mathscinet  zmath
    11. G. B. Shabat, “A system of equations of S. P. Novikov”, Funct. Anal. Appl., 14:2 (1980), 158–160  mathnet  crossref  mathscinet  zmath
    12. I. M. Gel'fand, I. Ya. Dorfman, “The Schouten Bracket and Hamiltonian operators”, Funct. Anal. Appl., 14:3 (1980), 223–226  mathnet  crossref  mathscinet  zmath  isi
    13. V. K. Mel'nikov, “Conservation laws for a class of systems of nonlinear evolution equations”, Funct. Anal. Appl., 15:1 (1981), 33–47  mathnet  crossref  mathscinet  zmath  isi
    14. I. M. Gel'fand, I. Ya. Dorfman, “Hamiltonian operators and infinite-dimensional Lie algebras”, Funct. Anal. Appl., 15:3 (1981), 173–187  mathnet  crossref  mathscinet  zmath  isi
    15. S. P. Novikov, “The Hamiltonian formalism and a many-valued analogue of Morse theory”, Russian Math. Surveys, 37:5 (1982), 1–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. P. G. Grinevich, “Rational solutions for the equation of commutation of differential operators”, Funct. Anal. Appl., 16:1 (1982), 15–19  mathnet  crossref  mathscinet  zmath  isi
    17. I. M. Gel'fand, I. Ya. Dorfman, “Hamiltonian operators and the classical Yang–Baxter equation”, Funct. Anal. Appl., 16:4 (1982), 241–248  mathnet  crossref  mathscinet  zmath  isi
    18. N. N. Bogolyubov, S. G. Gindikin, A. A. Kirillov, A. N. Kolmogorov, S. P. Novikov, L. D. Faddeev, “Izrail' Moiseevich Gel'fand (on his seventieth birthday)”, Russian Math. Surveys, 38:6 (1983), 145–153  mathnet  crossref  mathscinet  zmath  adsnasa
    19. V. K. Mel'nikov, “Some new nonlinear evolution equations integrable by the inverse problem method”, Math. USSR-Sb., 49:2 (1984), 461–489  mathnet  crossref  mathscinet  zmath
    20. V. V. Trofimov, A. T. Fomenko, “Liouville integrability of Hamiltonian systems on Lie algebras”, Russian Math. Surveys, 39:2 (1984), 1–67  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    21. O. I. Mokhov, “The Hamiltonian property of an evolutionary flow on the set of stationary points of its integral”, Russian Math. Surveys, 39:4 (1984), 133–134  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. A. V. Mikhailov, A. B. Shabat, “Integrability conditions for systems of two equations of the form $u_t+A(u)u_{xx}+F(u,u_x)$. I”, Theoret. and Math. Phys., 62:2 (1985), 107–122  mathnet  crossref  mathscinet  zmath  isi
    23. O. I. Mokhov, “On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral”, Math. USSR-Izv., 31:3 (1988), 657–664  mathnet  crossref  mathscinet  zmath
    24. A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, “The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems”, Russian Math. Surveys, 42:4 (1987), 1–63  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    25. A. P. Veselov, “Integrable discrete-time systems and difference operators”, Funct. Anal. Appl., 22:2 (1988), 83–93  mathnet  crossref  mathscinet  zmath  isi
    26. S. L. Luk'yanov, “Quantization of the Gel'fand?Dikii brackets”, Funct. Anal. Appl., 22:4 (1988), 255–262  mathnet  crossref  mathscinet  zmath  isi
    27. V. Yu. Ovsienko, B. A. Khesin, “Symplectic leaves of the Gel'fand–Dikii brackets and homotopy classes of nondegenerate curves”, Funct. Anal. Appl., 24:1 (1990), 33–40  mathnet  crossref  mathscinet  zmath  isi
    28. A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    29. Theoret. and Math. Phys., 96:2 (1993), 879–973  mathnet  crossref  mathscinet  zmath  isi
    30. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    31. A. N. Parshin, “On a Ring of Formal Pseudodifferential Operators”, Proc. Steklov Inst. Math., 224 (1999), 266–280  mathnet  mathscinet  zmath
    32. Kanehisa Takasaki, “Hamiltonian Structure of PI Hierarchy”, SIGMA, 3 (2007), 042, 32 pp.  mathnet  crossref  mathscinet  zmath
    33. Badanin A., Korotyaev E.L., “Even Order Periodic Operators on the Real Line”, Int Math Res Not, 2012, no. 5, 1143–1194  isi
    34. A. V. Domrin, “On holomorphic solutions of equations of Korteweg–de Vries type”, Trans. Moscow Math. Soc., 73 (2012), 193–206  mathnet  crossref  mathscinet  zmath  elib
    35. J. Atkinson, S. B. Lobb, F. W. Nijhoff, “An integrable multicomponent quad-equation and its Lagrangian formulation”, Theoret. and Math. Phys., 173:3 (2012), 1644–1653  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    36. A. B. Zheglov, “On rings of commuting partial differential operators”, St. Petersburg Math. J., 25:5 (2014), 775–814  mathnet  crossref  mathscinet  zmath  isi  elib
    37. V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, Theoret. and Math. Phys., 181:2 (2014), 1367–1382  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    38. Ufa Math. J., 8:2 (2016), 112–118  mathnet  crossref  isi  elib
    39. Wu Ch.-Zh., “Tau Functions and Virasoro Symmetries For Drinfeld-Sokolov Hierarchies”, Adv. Math., 306 (2017), 603–652  crossref  isi
    40. Liu K., Vakil R., Xu H., “Formal Pseudodifferential Operators and Witten'S R-Spin Numbers”, J. Reine Angew. Math., 728 (2017), 1–33  crossref  isi
    41. I. T. Habibullin, A. R. Khakimova, “A direct algorithm for constructing recursion operators and Lax pairs for integrable models”, Theoret. and Math. Phys., 196:2 (2018), 1200–1216  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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