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Mat. Zametki, 1998, Volume 63, Issue 4, Pages 509–521 (Mi mz1311)  

This article is cited in 9 scientific papers (total in 9 papers)

Extensions of Laguerre operators in indefinite inner product spaces

V. A. Derkach

Donetsk National University

Abstract: The Laguerre–Sonin polynomials $L_n^{(\alpha)}$ are orthogonal in linear spaces with indefinite inner product if $\alpha<-1$. We construct the completion $\Pi(\alpha)$ of this space and describe self-adjoint extensions of the Laguerre operator $l(y)=xy"+(1+\alpha-x)y'$, $\alpha<-1$, in the space $\Pi(\alpha)$. In particular, we write out the self-adjoint extension of the Laguerre operator whose eigenfunctions coincide with the Laguerre–Sonin polynomials and form an orthogonal basis in $\Pi(\alpha)$.

DOI: https://doi.org/10.4213/mzm1311

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English version:
Mathematical Notes, 1998, 63:4, 449–459

Bibliographic databases:

UDC: 517.98
Received: 13.05.1996
Revised: 23.10.1997

Citation: V. A. Derkach, “Extensions of Laguerre operators in indefinite inner product spaces”, Mat. Zametki, 63:4 (1998), 509–521; Math. Notes, 63:4 (1998), 449–459

Citation in format AMSBIB
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\paper Extensions of Laguerre operators in indefinite inner product spaces
\jour Mat. Zametki
\yr 1998
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\issue 4
\pages 509--521
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\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 4
\pages 449--459
\crossref{https://doi.org/10.1007/BF02311247}
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    This publication is cited in the following articles:
    1. D. A. Leites, A. N. Sergeev, “Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices”, Theoret. and Math. Phys., 123:2 (2000), 582–608  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Dijksma, A, “Singular point-like perturbations of the Bessel operator in a Pontryagin space”, Journal of Differential Equations, 164:1 (2000), 49  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Derkach, V, “Rank one perturbations in a Pontryagin space with one negative square”, Journal of Functional Analysis, 188:2 (2002), 317  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Dijksma A., Shondin Y., “Singular Point-Like Perturbations of the Laguerre Operator in a Pontryagin Space”, Operator Methods in Ordinary and Partial Differential Equations, Operator Theory : Advances and Applications, 132, eds. Albeverio S., Elander N., Everitt W., Kurasov P., Birkhauser Verlag Ag, 2002, 141–181  mathscinet  zmath  isi
    5. Dijksma, A, “Rank one perturbations at infinite coupling in Pontryagin spaces”, Journal of Functional Analysis, 209:1 (2004), 206  crossref  mathscinet  zmath  isi  scopus
    6. Fulton C., Langer H., “Sturm-Liouville Operators with Singularities and Generalized Nevanlinna Functions”, Complex Anal. Oper. Theory, 4:2 (2010), 179–243  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Kostenko A., Teschl G., “On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schrodinger Operators”, J. Differ. Equ., 250:9 (2011), 3701–3739  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    8. Pitelli Joao Paulo M., Saa A., “Quantum Singularities in Horava-Lifshitz Cosmology”, Phys. Rev. D, 86:6 (2012), 063506  crossref  adsnasa  isi  elib  scopus  scopus
    9. Kostenko A., Teschl G., “Spectral Asymptotics for Perturbed Spherical Schrodinger Operators and Applications to Quantum Scattering”, Commun. Math. Phys., 322:1 (2013), 255–275  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
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