Singular invariant hyperfunctions on the space of complex and quaternion Hermitian matrices. (English) Zbl 0994.46010

Muro, Masakazu

J. Math. Soc. Japan 53, No. 3, 589-602 (2001).

The author continues the study on invariant hyperfunctions on matrix spaces, initiated in a previous paper. The emphasis here is on hyperfunctions on the space of \(n\times n\) Hermitian matrices with complex, and quaternion elements. An algorithm for determining the orders of poles of complex powers of the determinant function, and their linear combinations, is presented. In the case when it consists of elements with rank strictly less than \(n\), it is found a description of the support of invariant hyperfunctions that are negative indexed coefficients of the Laurent expansion of linear combinations of complex powers of the determinant function.

Reviewer: Thomas V.Tonev (Missoula/Montana)

MSC:

46F15	Hyperfunctions, analytic functionals
20G20	Linear algebraic groups over the reals, the complexes, the quaternions
11E39	Bilinear and Hermitian forms
32A45	Hyperfunctions

Keywords:

invariant hyperfunctions on matrix spaces; Hermitian matrices; determinant function; Laurent expansion