Journal of Lie Theory Vol. 14, No. 1, pp. 111140 (2004) 

Algorithmic Construction of Hyperfunction Solutions to Invariant Differential Equations on the Space of Real Symmetric MatricesMasakazu MuroMasakazu MuroGifu University, Yanagito 11, Gifu 5011193,JAPAN muro@cc.gifuu.ac.jp Abstract: This is the second paper on invariant hyperfunction solutions of invariant linear differential equations on the vector space of $n \times n$ real symmetric matrices. In the preceding paper [Invariant hyperfunction solutions to invariant differential equations on the space of real symmetric matrices, J. Funct. Anal., 193 (2002), 346384], we proved that every invariant hyperfunction solution is expressed as a linear combination of Laurent expansion coefficients of the complex power of the determinant function with respect to the parameter. Fundamental properties of the complex power have been investigated in [Tôhoku Math. J. (2) {\bf51} (1999), 329364]. In this paper, we give algorithms to determine the space of invariant hyperfunction solutions and apply the algorithms to some examples. These algorithms enable us to compute in a fully constructive way all the invariant hyperfunction solutions for all the invariant differential operators in terms of Laurent expansion coefficients of the complex power of the determinant function. Keywords: invariant hyperfunctions, symmetric matrix spaces, linear differential equations Classification (MSC2000): 22E45, 58J15; 35A27 Full text of the article:
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