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Mat. Zametki, 1975, Volume 17, Issue 1, Pages 41–48 (Mi mz7221)  

This article is cited in 28 scientific papers (total in 28 papers)

Extensions of symmetric operators and symmetric binary relations

A. N. Kochubei

Abstract: Various classes of extensions of symmetric operators with equal (finite or infinite) defect numbers are described in terms of abstract boundary conditions. The dual problem of the description of extensions of a symmetric binary relation is also considered.

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English version:
Mathematical Notes, 1975, 17:1, 25–28

Bibliographic databases:

UDC: 513.88
Received: 20.02.1974

Citation: A. N. Kochubei, “Extensions of symmetric operators and symmetric binary relations”, Mat. Zametki, 17:1 (1975), 41–48; Math. Notes, 17:1 (1975), 25–28

Citation in format AMSBIB
\by A.~N.~Kochubei
\paper Extensions of symmetric operators and symmetric binary relations
\jour Mat. Zametki
\yr 1975
\vol 17
\issue 1
\pages 41--48
\jour Math. Notes
\yr 1975
\vol 17
\issue 1
\pages 25--28

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    This publication is cited in the following articles:
    1. V. M. Bruk, “On a class of boundary value problems with spectral parameter in the boundary condition”, Math. USSR-Sb., 29:2 (1976), 186–192  mathnet  crossref  mathscinet  zmath  isi
    2. A. N. Kochubei, “Symmetric operators commuting with a family of unitary operators”, Funct. Anal. Appl., 13:4 (1979), 300–301  mathnet  crossref  mathscinet  zmath
    3. A. N. Kochubei, “Elliptic operators with boundary conditions on a subset of measure zero”, Funct. Anal. Appl., 16:2 (1982), 137–139  mathnet  crossref  mathscinet  zmath  isi
    4. B. P. Allakhverdiev, “Extensions of symmetric Schrodinger operators with matrix potentials”, Izv. Math., 59:1 (1995), 45–62  mathnet  crossref  mathscinet  zmath  isi
    5. Pankrashkin, K, “Resolvents of self-adjoint extensions with mixed boundary conditions”, Reports on Mathematical Physics, 58:2 (2006), 207  crossref  isi
    6. V. M. Bruk, “On spaces of boundary values for relations generated by a formally selfadjoint expression and a nonnegative operator function”, Zhurn. matem. fiz., anal., geom., 2:3 (2006), 268–277  mathnet  mathscinet  zmath  elib
    7. V. M. Bruk, “Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression”, Russian Math. (Iz. VUZ), 52:11 (2008), 10–22  mathnet  crossref  mathscinet  zmath  elib
    8. Bruning, J, “Spectra of self-adjoint extensions and applications to solvable Schrödinger operators”, Reviews in Mathematical Physics, 20:1 (2008), 1  crossref  isi
    9. V. M. Bruk, “On linear relations generated by nonnegative operator function and degenerate elliptic differential-operator expression”, Zhurn. matem. fiz., anal., geom., 5:2 (2009), 123–144  mathnet  mathscinet  zmath  elib
    10. 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, ed. Ball J. Bolotnikov V. Helton J. Rodman L. Spitkovsky I., Birkhauser Verlag Ag, 2010, 247–287  crossref  isi
    11. 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  isi
    12. M. I. Belishev, M. N. Demchenko, “Dynamical system with boundary control associated with symmetric semi-bounded operator”, J. Math. Sci. (N. Y.), 194:1 (2013), 8–20  mathnet  crossref  mathscinet
    13. Goryunov A.S. Mikhailets V.A., “Regularization of Two-Term Differential Equations with Singular Coefficients by Quasiderivatives”, Ukr. Math. J., 63:9 (2012), 1361–1378  isi
    14. Yu. M. Arlinskii, A. B. Popov, “$m$-Accretive extensions of a sectorial operator”, Sb. Math., 204:8 (2013), 1085–1121  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. Allahverdiev B.P., “Extensions of Symmetric Second-Order Difference Operators with Matrix Coefficients”, J. Differ. Equ. Appl., 19:5 (2013), 839–849  crossref  isi
    16. Goriunov A. Mikhailets V. Pankrashkin K., “Formally Self-Adjoint Quasi-Differential Operators and Boundary-Value Problems”, Electron. J. Differ. Equ., 2013, 101  isi
    17. V. M. Bruk, “On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case”, Zhurn. matem. fiz., anal., geom., 10:2 (2014), 163–188  mathnet  crossref  mathscinet
    18. V. M. Bruk, “Dissipative expansions of a symmetric relation generated by a system of integral equations with operator measures”, Russian Math. (Iz. VUZ), 58:12 (2014), 7–22  mathnet  crossref
    19. Ufa Math. J., 7:2 (2015), 115–136  mathnet  crossref  isi  elib
    20. Konstantinov O.O., “Two-Term Differential Equations With Matrix Distributional Coefficients”, Ukr. Math. J., 67:5 (2015), 711–722  crossref  isi
    21. Behrndt J., Gesztesy F., Holden H., Nichols R., “Dirichlet-to-Neumann maps, abstract Weyl–Titchmarsh M -functions, and a generalized index of unbounded meromorphic operator-valued functions”, J. Differ. Equ., 261:6 (2016), 3551–3587  crossref  mathscinet  zmath  isi  elib  scopus
    22. M. I. Belishev, S. A. Siminov, “Wave model of the Sturm–Liouville operator on the half-line”, St. Petersburg Math. J., 29:2 (2018), 227–248  mathnet  crossref  mathscinet  isi  elib
    23. J. Math. Sci. (N. Y.), 238:5 (2019), 701–714  mathnet  crossref
    24. T. A. Bolokhov, “Resolvents of selfadjoint extensions of the Laplace operator on the solenoidal subspace”, J. Math. Sci. (N. Y.), 243:6 (2019), 835–840  mathnet  crossref
    25. S. A. Simonov, “Wave model of the Sturm–Liouville operator on an interval”, J. Math. Sci. (N. Y.), 243:5 (2019), 783–807  mathnet  crossref
    26. V. M. Bruk, “Generalized resolvents of operators generated by integral equations”, Probl. anal. Issues Anal., 7(25):2 (2018), 20–38  mathnet  crossref  elib
    27. Allahverdiev B.P., “Spectral Analysis of Singular Matrix-Valued Sturm-Liouville Operators”, Mediterr. J. Math., 16:4 (2019), 83  crossref  isi
    28. Trans. Moscow Math. Soc., 80 (2019), 251–294  mathnet  crossref  elib
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