Nagoya Mathematical Journal

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

Masakazu Muro

Abstract

Fundamental calculations on singular invariant hyperfunctions on the $n \times n$ square matrix space and on the $2n \times 2n$ 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.

Article information

Source
Nagoya Math. J., Volume 169 (2003), 19-75.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114631809

Mathematical Reviews number (MathSciNet)
MR1962523

Zentralblatt MATH identifier
1068.11077

Citation

Muro, Masakazu. Singular invariant hyperfunctions on the square matrix space and the alternating matrix space. Nagoya Math. J. 169 (2003), 19--75. https://projecteuclid.org/euclid.nmj/1114631809

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