The convolution structure for Jacobi function expansions |
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| Authors: | Mogens Flensted-Jensen and Tom Koornwinder |
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| Affiliation: | (1) Matematisk Institut, Universitetparken 5, DK-2100 Copenhagen, Denmark;(2) Mathematisch Centrum, 2e Boerhaavestraat 49, Amsterdam, Netherlands |
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| Abstract: | The product ϕ λ (α,β) (t1)ϕ λ (α,β) (t2) of two Jacobi functions is expressed as an integral in terms of ϕ λ (α,β) (t3) with explicit non-negative kernel, when α≧β≧−1/2. The resulting convolution structure for Jacobi function expansions is studied. For special values of α and β the results are known from the theory of symmetric spaces. |
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