## 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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### References:

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