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Functional equations and matrix-valued spherical functions

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Summary.

We show that any solution of a certain functional equation, generalizing such equations as Wilson’s, Levi-Cività’s, Gajda’s and the sine addition equation, can be expressed in terms of a matrix-valued spherical function. We compute this matrix-valued function for solutions of various functional equations, and use it to solve the equations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Aarhus, DK-8000, Aarhus C, Denmark

    Henrik Stetkær

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  1. Henrik Stetkær
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Correspondence to Henrik Stetkær.

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Manuscript received: December 12, 2003 and, in final form, March 25, 2004.

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Stetkær, H. Functional equations and matrix-valued spherical functions. Aequ. math. 69, 271–292 (2005). https://doi.org/10.1007/s00010-004-2754-6

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  • DOI: https://doi.org/10.1007/s00010-004-2754-6

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