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...
Збережено в:
| Видавець: | Інститут математики НАН України |
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| Дата: | 2016 |
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| 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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| 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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