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Algebra i Analiz, 2003, Volume 15, Issue 3, Pages 1–77 (Mi aa793)  

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

Expository Surveys

Spectral theory of operator measures in Hilbert space

M. M. Malamud, S. M. Malamud

Donetsk National University

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English version:
St. Petersburg Mathematical Journal, 2004, 15:3, 323–373

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Received: 19.06.2002

Citation: M. M. Malamud, S. M. Malamud, “Spectral theory of operator measures in Hilbert space”, Algebra i Analiz, 15:3 (2003), 1–77; St. Petersburg Math. J., 15:3 (2004), 323–373

Citation in format AMSBIB
\by M.~M.~Malamud, S.~M.~Malamud
\paper Spectral theory of operator measures in Hilbert space
\jour Algebra i Analiz
\yr 2003
\vol 15
\issue 3
\pages 1--77
\jour St. Petersburg Math. J.
\yr 2004
\vol 15
\issue 3
\pages 323--373

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    This publication is cited in the following articles:
    1. A. S. Kostenko, “The Krein string and characteristic functions of non-self-adjoint operators”, J. Math. Sci. (N. Y.), 139:2 (2006), 6425–6436  mathnet  crossref  mathscinet  zmath
    2. Albeverio S., Brasche J. F., Malamud M. M., Neidhardt H., “Inverse spectral theory for symmetric operators with several gaps: scalar-type Weyl functions”, J. Funct. Anal., 228:1 (2005), 144–188  crossref  mathscinet  zmath  isi  elib  scopus
    3. Derkach V., Hassi S., Malamud M., de Snoo H., “Boundary relations and their Weyl families”, Trans. Amer. Math. Soc., 358:12 (2006), 5351–5400 (electronic)  crossref  mathscinet  zmath  isi  elib  scopus
    4. Kostenko A.S., “Spectral Analysis of Some Indefinite Sturm-Liouville Operators”, Operator Theory 20, Proceedings, 2006, 131–141  mathscinet  zmath  isi
    5. Karabash I. M., Malamud M. M., “Indefinite Sturm-Liouville operators $(\mathrm{sgn}x)(-\frac{d^2}{dx^2}+q(x))$ with finite-zone potentials”, Oper. Matrices, 1:3 (2007), 301–368  crossref  mathscinet  zmath  isi
    6. Jung I.B., Stochel J., “Subnormal operators whose adjoints have rich point spectrum”, Journal of Functional Analysis, 255:7 (2008), 1797–1816  crossref  mathscinet  zmath  isi  scopus
    7. Alpay D., Behrndt J., “Generalized $Q$-functions and Dirichlet-to-Neumann maps for elliptic differential operators”, J. Funct. Anal., 257:6 (2009), 1666–1694  crossref  mathscinet  zmath  isi  elib  scopus
    8. Behrndt J., Hassi S., de Snoo H., “Boundary Relations, Unitary Colligations, and Functional Models”, Complex Anal. Oper. Theory, 3:1 (2009), 57–98  crossref  mathscinet  zmath  isi  elib  scopus
    9. Behrndt J., “Realization of Nonstrict Matrix Nevanlinna Functions as Weyl Functions of Symmetric Operators in Pontryagin Spaces”, Proceedings of the American Mathematical Society, 137:8 (2009), 2685–2696  crossref  mathscinet  zmath  isi  scopus
    10. Derkach V., “Abstract Interpolation Problem in Nevanlinna Classes”, Modern Analysis and Applications: Mark Krein Centenary Conference. Vol. 1: Operator Theory and Related Topics, Operator Theory Advances and Applications, 190, 2009, 197–236  mathscinet  zmath  isi
    11. I. V. Orlov, “Banach–Zaretsky theorem for compactly absolutely continuous mappings”, Journal of Mathematical Sciences, 180:6 (2012), 710–730  mathnet  crossref  mathscinet
    12. Zagorodnyuk S.M., “On the Strong Matrix Hamburger Moment Problem”, Ukrainian Mathematical Journal, 62:4 (2010), 537–551  crossref  mathscinet  zmath  isi  elib  scopus
    13. Behrndt J., Langer M., “On the adjoint of a symmetric operator”, Journal of the London Mathematical Society-Second Series, 82:3 (2010), 563–580  crossref  mathscinet  zmath  isi  scopus
    14. Aleksandrov A.B., Peller V.V., “Operator Holder-Zygmund functions”, Advances in Mathematics, 224:3 (2010), 910–966  crossref  mathscinet  zmath  isi  scopus
    15. Behrndt J., Malamud M.M., Neidhardt H., “Finite Rank Perturbations, Scattering Matrices and Inverse Problems”, Recent Advances in Operator Theory in Hilbert and Krein Spaces, Operator Theory Advances and Applications, 198, 2010, 61–85  mathscinet  zmath  isi
    16. Karabash I.M., “A Functional Model, Eigenvalues, and Finite Singular Critical Points for Indefinite Sturm-Liouville Operators”, Topics in Operator Theory. Vol. 2: Systems and Mathematical Physics, Operator Theory Advances and Applications, 203, 2010, 247–287  mathscinet  zmath  isi
    17. Malamud M.M., Neidhardt H., “On the unitary equivalence of absolutely continuous parts of self-adjoint extensions”, Journal of Functional Analysis, 260:3 (2011), 613–638  crossref  mathscinet  zmath  isi  scopus
    18. A. B. Aleksandrov, V. V. Peller, “Functions of perturbed dissipative operators”, St. Petersburg Math. J., 23:2 (2012), 209–238  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    19. Zagorodnyuk S.M., “Truncated Matrix Trigonometric Problem of Moments: Operator Approach”, Ukrainian Math J, 63:6 (2011), 914–926  crossref  mathscinet  zmath  isi  elib  scopus
    20. Behrndt J., Hassi S., de Snoo H., Wietsma R., “Square-integrable solutions and Weyl functions for singular canonical systems”, Math Nachr, 284:11–12 (2011), 1334–1384  crossref  mathscinet  zmath  isi  elib  scopus
    21. Mogilevskii V., “Minimal Spectral Functions of an Ordinary Differential Operator”, Proc. Edinb. Math. Soc., 55:Part 3 (2012), 731–769  crossref  mathscinet  zmath  isi  elib  scopus
    22. Malamud M., Neidhardt H., “Sturm-Liouville Boundary Value Problems with Operator Potentials and Unitary Equivalence”, J. Differ. Equ., 252:11 (2012), 5875–5922  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    23. Zagorodnyuk S.M., “The Matrix Stieltjes Moment Problem: a Description of All Solutions”, N. Y. J. Math., 18 (2012), 479–497  mathscinet  zmath  isi  elib
    24. Pankrashkin K., “Unitary Dimension Reduction for a Class of Self-Adjoint Extensions with Applications to Graph-Like Structures”, J. Math. Anal. Appl., 396:2 (2012), 640–655  crossref  mathscinet  zmath  isi  elib  scopus
    25. Pankrashkin K., “An Example of Unitary Equivalence Between Self-Adjoint Extensions and their Parameters”, J. Funct. Anal., 265:11 (2013), 2910–2936  crossref  mathscinet  zmath  isi  elib  scopus
    26. Albeverio S. Malamud M. Mogilevskii V., “On Titchmarsh-Weyl Functions and Eigenfunction Expansions of First-Order Symmetric Systems”, Integr. Equ. Oper. Theory, 77:3 (2013), 303–354  crossref  mathscinet  zmath  isi  elib  scopus
    27. Gesztesy F. Weikard R. Zinchenko M., “On a Class of Model Hilbert Spaces”, Discret. Contin. Dyn. Syst., 33:11-12, SI (2013), 5067–5088  crossref  mathscinet  zmath  isi  elib  scopus
    28. Gesztesy F. Weikard R. Zinchenko M., “On Spectral Theory for Schrodinger Operators with Operator-Valued Potentials”, J. Differ. Equ., 255:7 (2013), 1784–1827  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    29. Gesztesy F., Weikard R., Zinchenko M., “Initial Value Problems and Weyl-Titchmarsh Theory for Schrodinger Operators with Operator-Valued Potentials”, Oper. Matrices, 7:2 (2013), 241–283  crossref  mathscinet  zmath  isi  elib  scopus
    30. Carlone R., Malamud M., Posilicano A., “On the Spectral Theory of Gesztesy-Seba Realizations of 1-D Dirac Operators with Point Interactions on a Discrete Set”, J. Differ. Equ., 254:9 (2013), 3835–3902  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    31. Hassi S., Malamud M., Mogilevskii V., “Unitary Equivalence of Proper Extensions of a Symmetric Operator and the Weyl Function”, Integr. Equ. Oper. Theory, 77:4 (2013), 449–487  crossref  mathscinet  zmath  isi  elib  scopus
    32. S. M. Zagorodnyuk, “On the Density of Polynomials in Some Spaces $L^2(M)$”, Math. Notes, 95:1 (2014), 53–66  mathnet  crossref  crossref  mathscinet  isi  elib
    33. A. B. Aleksandrov, V. V. Peller, “Operator Lipschitz functions”, Russian Math. Surveys, 71:4 (2016), 605–702  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    34. Hatamleh R., Zolotarev V.A., “Jacobi Operators and Orthonormal Matrix-Valued Polynomials. i”, Ukr. Math. J., 69:2 (2017), 269–282  crossref  mathscinet  isi  scopus
    35. Hatamleh R., Zolotarev V.A., “Jacobi Operators and Orthonormal Matrix-Valued Polynomials. II”, Ukr. Math. J., 69:6 (2017), 970–985  crossref  mathscinet  isi  scopus
    36. Behrndt J., Langer M., Lotoreichik V., Rohleder J., “Spectral Enclosures For Non-Self-Adjoint Extensions of Symmetric Operators”, J. Funct. Anal., 275:7 (2018), 1808–1888  crossref  mathscinet  zmath  isi  scopus
    37. Malamud M.M. Neidhardt H. Peller V.V., “Absolute Continuity of Spectral Shift”, J. Funct. Anal., 276:5 (2019), 1575–1621  crossref  mathscinet  zmath  isi  scopus
    38. Gesztesy F., Naboko S.N., Weikard R., Zinchenko M., “Donoghue-Type M-Functions For Schrodinger Operators With Operator-Valued Potentials”, J. Anal. Math., 137:1 (2019), 373–427  crossref  isi
    39. Malamud M.M., “On Singular Spectrum of Finite-Dimensional Perturbations (Toward the Aronszajn-Donoghue-Kac Theory)”, Dokl. Math., 100:1 (2019), 358–362  crossref  isi  scopus
    40. Derkach V., Dym H., “Functional Models For Entire Symmetric Operators in Rigged de Branges Pontryagin Spaces”, J. Funct. Anal., 280:2 (2021), 108776  crossref  mathscinet  isi
    41. V. S. Budyka, M. M. Malamud, K. A. Mirzoev, “Indeksy defekta blochnykh matrits Yakobi: obzor”, Posvyaschaetsya pamyati professora N.D. Kopachevskogo, SMFN, 67, no. 2, Rossiiskii universitet druzhby narodov, M., 2021, 237–254  mathnet  crossref
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