Shell Polynomials and Dual Birth-Death Processes
This paper aims to clarify certain aspects of the relations between birth-death processes, measures solving a Stieltjes moment problem, and sets of parameters defining polynomial sequences that are orthogonal with respect to such a measure. Besides giving an overview of the basic features of these r...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147745 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Shell Polynomials and Dual Birth-Death Processes / Erik A. van Doorn // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862561839962914816 |
|---|---|
| author | Erik A. van Doorn |
| author_facet | Erik A. van Doorn |
| citation_txt | Shell Polynomials and Dual Birth-Death Processes / Erik A. van Doorn // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper aims to clarify certain aspects of the relations between birth-death processes, measures solving a Stieltjes moment problem, and sets of parameters defining polynomial sequences that are orthogonal with respect to such a measure. Besides giving an overview of the basic features of these relations, revealed to a large extent by Karlin and McGregor, we investigate a duality concept for birth-death processes introduced by Karlin and McGregor and its interpretation in the context of shell polynomials and the corresponding orthogonal polynomials. This interpretation leads to increased insight in duality, while it suggests a modification of the concept of similarity for birth-death processes.
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| first_indexed | 2025-11-25T23:28:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147745 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T23:28:43Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Erik A. van Doorn 2019-02-15T19:05:54Z 2019-02-15T19:05:54Z 2016 Shell Polynomials and Dual Birth-Death Processes / Erik A. van Doorn // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C05; 60J80; 44A60 DOI:10.3842/SIGMA.2016.049 https://nasplib.isofts.kiev.ua/handle/123456789/147745 This paper aims to clarify certain aspects of the relations between birth-death processes, measures solving a Stieltjes moment problem, and sets of parameters defining polynomial sequences that are orthogonal with respect to such a measure. Besides giving an overview of the basic features of these relations, revealed to a large extent by Karlin and McGregor, we investigate a duality concept for birth-death processes introduced by Karlin and McGregor and its interpretation in the context of shell polynomials and the corresponding orthogonal polynomials. This interpretation leads to increased insight in duality, while it suggests a modification of the concept of similarity for birth-death processes. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
 The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Shell Polynomials and Dual Birth-Death Processes Article published earlier |
| spellingShingle | Shell Polynomials and Dual Birth-Death Processes Erik A. van Doorn |
| title | Shell Polynomials and Dual Birth-Death Processes |
| title_full | Shell Polynomials and Dual Birth-Death Processes |
| title_fullStr | Shell Polynomials and Dual Birth-Death Processes |
| title_full_unstemmed | Shell Polynomials and Dual Birth-Death Processes |
| title_short | Shell Polynomials and Dual Birth-Death Processes |
| title_sort | shell polynomials and dual birth-death processes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147745 |
| work_keys_str_mv | AT erikavandoorn shellpolynomialsanddualbirthdeathprocesses |