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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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147745 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1477452019-02-16T01:25:26Z Shell Polynomials and Dual Birth-Death Processes Erik A. van Doorn 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147745 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Erik A. van Doorn |
| spellingShingle |
Erik A. van Doorn Shell Polynomials and Dual Birth-Death Processes Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Erik A. van Doorn |
| author_sort |
Erik A. van Doorn |
| title |
Shell Polynomials and Dual Birth-Death Processes |
| title_short |
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_sort |
shell polynomials and dual birth-death processes |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147745 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT erikavandoorn shellpolynomialsanddualbirthdeathprocesses |
| first_indexed |
2023-05-20T17:28:12Z |
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2023-05-20T17:28:12Z |
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1796153365119369216 |