On the completeness of the set of eigenvectors of a certain class of self-adjoint finite difference operators

M. A. El-Gebeily; K. M. Furati

doi:10.1093/imamat/65.1.29

On the completeness of the set of eigenvectors of a certain class of self-adjoint finite difference operators

M. A. El-Gebeily^*
, K. M. Furati

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we study a special class of formally self-adjoint finite difference operators acting on infinite sequences. Such operators give rise to self-adjoint ones acting on appropriate Hilbert spaces. We prove that the latter operators possess a set of orthonormal eigenvectors complete in the Hilbert space.

Original language	English
Pages (from-to)	29-43
Number of pages	15
Journal	IMA Journal of Applied Mathematics
Volume	65
Issue number	1
DOIs	https://doi.org/10.1093/imamat/65.1.29
State	Published - Aug 2000

Bibliographical note

Funding Information:
The authors are grateful for the financial support provided by King Fahd University of Petroleum and Minerals under research grant MS/numerical/190.

ASJC Scopus subject areas

Applied Mathematics

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10.1093/imamat/65.1.29

Cite this

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title = "On the completeness of the set of eigenvectors of a certain class of self-adjoint finite difference operators",

abstract = "In this paper we study a special class of formally self-adjoint finite difference operators acting on infinite sequences. Such operators give rise to self-adjoint ones acting on appropriate Hilbert spaces. We prove that the latter operators possess a set of orthonormal eigenvectors complete in the Hilbert space.",

author = "El-Gebeily, \{M. A.\} and Furati, \{K. M.\}",

note = "Funding Information: The authors are grateful for the financial support provided by King Fahd University of Petroleum and Minerals under research grant MS/numerical/190.",

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AU - Furati, K. M.

N1 - Funding Information: The authors are grateful for the financial support provided by King Fahd University of Petroleum and Minerals under research grant MS/numerical/190.

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N2 - In this paper we study a special class of formally self-adjoint finite difference operators acting on infinite sequences. Such operators give rise to self-adjoint ones acting on appropriate Hilbert spaces. We prove that the latter operators possess a set of orthonormal eigenvectors complete in the Hilbert space.

AB - In this paper we study a special class of formally self-adjoint finite difference operators acting on infinite sequences. Such operators give rise to self-adjoint ones acting on appropriate Hilbert spaces. We prove that the latter operators possess a set of orthonormal eigenvectors complete in the Hilbert space.

UR - https://www.scopus.com/pages/publications/0034250923

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DO - 10.1093/imamat/65.1.29

M3 - Article

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JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 1

ER -

On the completeness of the set of eigenvectors of a certain class of self-adjoint finite difference operators

Abstract

Bibliographical note

ASJC Scopus subject areas

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