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Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations
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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Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations
Інший ID:
2010 Mathematics Subject Classification: 33C50; 42C10
DOI:10.3842/SIGMA.2016.020
DOI:10.3842/SIGMA.2016.020
Посилання:
Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations / C. Martínez, M.A. Piñar // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 12 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.
We gratefully thanks the anonymous referees for their valuable comments and suggestions. This
work has been partially supported by DGICYT, Ministerio de Econom´ıa y Competitividad
(MINECO) of Spain and the European Regional Development Fund (ERDF) through grants
MTM2011–28952–C02–02, MTM2014–53171–P, Reseach Project P11-FQM-7276 and Research
Group FQM-384 from Junta de Andaluc´ıa.
Дата:
2016
Переглядів:
650
Завантажень:
192
Анотація:
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of orthogonal polynomials. Then, using the representation of these polynomials in terms of spherical harmonics, algebraic and differential properties will be deduced.
