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This article is cited in 9 scientific papers (total in 9 papers)
Spherical Functions of Fundamental $K$-Types Associated with the $n$-Dimensional Sphere
Juan Alfredo Tirao, Ignacio Nahuel Zurrián CIEM-FaMAF, Universidad Nacional de Córdoba, Argentina
Abstract:
In this paper, we describe the irreducible spherical functions of fundamental $K$-types associated with the pair $(G,K)=({\mathrm{SO}}(n+1),{\mathrm{SO}}(n))$ in terms of matrix hypergeometric functions. The output of this description is that the irreducible spherical functions of the same $K$-fundamental type are encoded in new examples of classical sequences of matrix-valued orthogonal polynomials, of size $2$ and $3$, with respect to a matrix-weight $W$ supported on $[0,1]$. Moreover, we show that $W$ has a second order symmetric hypergeometric operator $D$.
Keywords:
matrix-valued spherical functions; matrix orthogonal polynomials; the matrix hypergeometric
operator; $n$-dimensional sphere.
Received: December 20, 2013; in final form June 20, 2014; Published online July 7, 2014
Citation:
Juan Alfredo Tirao, Ignacio Nahuel Zurrián, “Spherical Functions of Fundamental $K$-Types Associated with the $n$-Dimensional Sphere”, SIGMA, 10 (2014), 071, 41 pp.
Linking options:
https://www.mathnet.ru/eng/sigma936 https://www.mathnet.ru/eng/sigma/v10/p71
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Abstract page: | 221 | Full-text PDF : | 53 | References: | 43 |
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