Root systems and hypergeometric functions III

E. M. Opdam

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Root systems and hypergeometric functions. I

G. J. Heckman, E. M. Opdam (1987)

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Root systems and hypergeometric functions IV

E. M. Opdam (1988)

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Root systems and hypergeometric functions. II

G. J. Heckman (1987)

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Dunkl operators

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Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group

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The Abel transform and shift operators

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The decomposability of operators relative to two subspaces

A. Katavolos, M. Lambrou, W. Longstaff (1993)

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Let M and N be nonzero subspaces of a Hilbert space H satisfying M ∩ N = {0} and M ∨ N = H and let T ∈ ℬ(H). Consider the question: If T leaves each of M and N invariant, respectively, intertwines M and N, does T decompose as a sum of two operators with the same property and each of which, in addition, annihilates one of the subspaces? If the angle between M and N is positive the answer is affirmative. If the angle is zero, the answer is still affirmative for finite rank operators but...

On the Faraut-Koranyi hypergeometric functions in rank two

Miroslav Engliš, Genkai Zhang (2004)

Annales de l’institut Fourier

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We give a complete description of the boundary behaviour of the generalized hypergeometric functions, introduced by Faraut and Koranyi, on Cartan domains of rank 2. The main tool is a new integral representation for some spherical polynomials, which may be of independent interest.