A study of resolvent set for a class of band operators with matrix elements

For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior o...

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Bibliographic Details
Main Author:	Osipov Andrey
Format:	Article
Language:	English
Published:	De Gruyter 2016-05-01
Series:	Concrete Operators
Subjects:	Band operators Difference Equations Weyl matrix, Orthogonal polynomials, Resolvent sets
Online Access:	http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0010/conop-2016-0010.xml?format=INT

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spelling	doaj-e59dfdb7ba4a459187cd995fb8bd8c6f2020-11-24T22:36:44ZengDe GruyterConcrete Operators2299-32822016-05-0131859310.1515/conop-2016-0010conop-2016-0010A study of resolvent set for a class of band operators with matrix elementsOsipov Andrey0Scientific-Research Institute for System Studies, Russian Academy of Sciences, Nakhimovskii pr. 36-1, Moscow, 117218, RussiaFor operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0010/conop-2016-0010.xml?format=INTBand operators Difference Equations Weyl matrix, Orthogonal polynomials, Resolvent sets
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Osipov Andrey
spellingShingle	Osipov Andrey A study of resolvent set for a class of band operators with matrix elements Concrete Operators Band operators Difference Equations Weyl matrix, Orthogonal polynomials, Resolvent sets
author_facet	Osipov Andrey
author_sort	Osipov Andrey
title	A study of resolvent set for a class of band operators with matrix elements
title_short	A study of resolvent set for a class of band operators with matrix elements
title_full	A study of resolvent set for a class of band operators with matrix elements
title_fullStr	A study of resolvent set for a class of band operators with matrix elements
title_full_unstemmed	A study of resolvent set for a class of band operators with matrix elements
title_sort	study of resolvent set for a class of band operators with matrix elements
publisher	De Gruyter
series	Concrete Operators
issn	2299-3282
publishDate	2016-05-01
description	For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.
topic	Band operators Difference Equations Weyl matrix, Orthogonal polynomials, Resolvent sets
url	http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0010/conop-2016-0010.xml?format=INT
work_keys_str_mv	AT osipovandrey astudyofresolventsetforaclassofbandoperatorswithmatrixelements AT osipovandrey studyofresolventsetforaclassofbandoperatorswithmatrixelements
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A study of resolvent set for a class of band operators with matrix elements

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