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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| Format: | Article |
| Language: | English |
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De Gruyter
2016-05-01
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| Series: | Concrete Operators |
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| Online Access: | http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0010/conop-2016-0010.xml?format=INT |
| _version_ | 1819240590250868736 |
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| author | Osipov Andrey |
| author_facet | Osipov Andrey |
| author_sort | Osipov Andrey |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-23T14:10:26Z |
| format | Article |
| id | doaj.art-e59dfdb7ba4a459187cd995fb8bd8c6f |
| institution | Directory Open Access Journal |
| issn | 2299-3282 |
| language | English |
| last_indexed | 2024-12-23T14:10:26Z |
| publishDate | 2016-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Concrete Operators |
| spelling | doaj.art-e59dfdb7ba4a459187cd995fb8bd8c6f2022-12-21T17:44:03ZengDe 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 |
| 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 |
| title | 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_short | 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 |
| 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 |