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A definition of boundary values of solutions of partial differential equations with regular singularities. (English) Zbl 0559.35007

Helgason’s conjecture states that any simultaneous eigenfunction of the invariant differential operators of a Riemannian symmetric space of non- compact type has a Poisson integral representation of a hyperfunction on its maximal boundary. The present paper introduces a new definition of the boundary values in an elementary way and gives several results concerning the definition, which are sufficient to solve the ”conjecture”.
Reviewer: T.Rassias

MSC:

35C15 Integral representations of solutions to PDEs
35A20 Analyticity in context of PDEs
46F15 Hyperfunctions, analytic functionals
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