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Singular invariant hyperfunctions on the square matrix space and the alternating matrix space

Published online by Cambridge University Press:  22 January 2016

Masakazu Muro
Masakazu Muro*
Affiliation:
Gifu University, Yanagito 1-1, Gifu, 501-1193, Japan, muro@cc.gifu-u.ac.jp
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Abstract

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Fundamental calculations on singular invariant hyperfunctions on the n ×n square matrix space and on the 2n × 2n alternating matrix space are considered in this paper. By expanding the complex powers of the determinant function or the Pfaffian function into the Laurent series with respect to the complex parameter, we can construct singular invariant hyperfunctions as their Laurent expansion coefficients. The author presents here the exact orders of the poles of the complex powers and determines the exact supports of the Laurent expansion coefficients. By applying these results, we prove that every quasi-relatively invariant hyperfunction can be expressed as a linear combination of the Laurent expansion coefficients of the complex powers and that every singular quasi-relatively invariant hyperfunction is in fact relatively invariant on the generic points of its support. In the last section, we give the formula of the Fourier transforms of singular invariant tempered distributions.

Keywords

22E4520G2011E39
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 169 , 2003 , pp. 19 - 75
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

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