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Shell Polynomials and Dual Birth-Death Processes
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12, випуск за цей рік
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Shell Polynomials and Dual Birth-Death Processes
Інший ID:
2010 Mathematics Subject Classification: 42C05; 60J80; 44A60
DOI:10.3842/SIGMA.2016.049
DOI:10.3842/SIGMA.2016.049
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
483
Завантажень:
263
Анотація:
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.
