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  Weyl function and spectral properties of self-adjoint extensions, Integral Eqs. Operator Theory 43 (2002) [2 citations — 1 self]

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by Johannes F. Brasche, Mark Malamud, Hagen Neidhardt
Integral Equations Operator Theory 43 (2002
http://www.ma.utexas.edu/mp_arc/c/01/01-183.ps.gz
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Abstract:

We characterize the spectra of self-adjoint extensions of a symmetric operator with equal deciency indices in terms of boundary values of their Weyl functions. A complete description is obtained for the point and absolutely continuous spectrum while for the singular continuous spectrum additional assumptions are needed. The results are illustrated by examples. 1

Citations

121 Bounded Analytic Functions – Garnett - 1981
51 The Markov moment problem and extremal problems – Krein, Nudelman - 1977
42 Expansions in eigenfunctions of selfadjoint operators – Berezanskii - 1968
35 Linear Operators. Part I: General Theory – Dunford, Schwartz - 1988
27 On exponential representations of analytic functions in the upper half-plane with positive imaginary part – Aronszajn, Donoghue - 1957
16 Introduction to H p spaces – Koosis - 1980
15 On the perturbation of spectra – Donoghue - 1965
14 On a problem of Weyl in the theory of singular Sturm-Liouville equations – Aronszajn - 1957
14 Generalized resolvents and the boundary value problems for Hermitian operators with gaps – Derkach, Malamud - 1991
11 On matrix-valued Herglotz functions – Gesztesy, Tsekanovskii - 2000
9 The extension theory of Hermitian operators and the moment problem – Derkach, Malamud - 1995
8 Theorie der linearen Operatoren im Hilbert Raum, Akademie-Verlag – Achieser, Glasmann - 1981
8 On defect subspaces and generalized resolvents of an Hermitian operator – Krein, Langer - 1971
5 On the point spectrum of self-adjoint extensions – Brasche, Neidhardt, et al. - 1993
4 On inverse spectral theory for self-adjoint extensions – Albeverio, Brasche, et al. - 1998
4 On the absolutely continuous spectrum of self-adjoint extensions – Brasche, Neidhardt - 1995
3 On the Weyl function and Hermitian operators with gaps, Dokl – Derkach, Malamud - 1987
3 Some applications of operator-valued Herglotz functions – Gesztesy, Kalton, et al. - 1997
2 Weyl function and singular continuous spectra of self-adjoint extensions – Brasche, Malamud, et al. - 2000
2 Boundary value problems for operator dierential equations – Gorbachuk, Gorbachuk - 1991
2 Uniqueness theorems for operator-valued functions with positive imaginary part and the singular spectrum, Ark – Naboko - 1987
1 Brasche, On spectra of self-adjoint extensions and generalized Schrdinger operators – F - 1995
1 A theorem of the Fatou type – Donoghue - 1963
1 Theory of functions with real variables, Izd – Natanson - 1974
1 Theory of integrals (Second revised edition – Saks - 1937
1 ber gewhnliche lineare Dierentialgleichungen mit singulren Stellen und ihre Eigenfunktionen, Gttinger Nachrichten – Weyl - 1909
1 ber gewhnliche Dierentialgleichungen mit Singularitten und die zugehrigen Entwicklungen willkrlicher Funktionen – Weyl - 1910