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Print ISSN : 0532-8721
Infinite-Variate Extensions of Krawtchouk Polynomials and Zonal Spherical Functions over a Local Field
Koei Kawamura
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2021 Volume 64 Issue 1 Pages 75-118

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Abstract

The multivariate Krawtchouk polynomials are orthogonal polynomials for the multinomial distribution, first defined by Griffiths in 1971. We construct infinite-variate extensions of them as complete orthogonal systems of specific weighted l2-spaces. We also give realizations of our infinite-variate extensions as zonal spherical functions on groups over a non-Archimedean local field. Some typical properties of Krawtchouk polynomials like duality, orthogonality and completeness are thus shed light from the point of view of zonal spherical functions.

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© 2021 by the Division of Functional Equations, The Mathematical Society of Japan
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