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Boundary value problems for Whittaker functions on real split semisimple Lie groups. (English) Zbl 0621.22011

Let G be a connected real split semisimple Lie group with finite center, and let \(G=KAN\) be an Iwasawa decomposition. Denote by B(G) the space of hyperfunctions on G. If \(\psi\) is a character of N, the space of Whittaker hyperfunctions B(G/N,\(\psi)\) is defined as \(\{\) \(f\in B(G)\), \(f(gn)=\psi (n)f(g)\) for \(g\in G\), \(n\in N\}\). The author studies the structure of the space of Whittaker hyperfunctions, using Oshima’s generalization of the notion of differential equations with regular singularities and their boundary values.
Reviewer: P.Godin

MSC:

22E30 Analysis on real and complex Lie groups
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
58J15 Relations of PDEs on manifolds with hyperfunctions
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