Generalized functions which are analytic with respect to some of their variables

Yu. A. Brychkov

Dorodnitsyn Computing Centre of the Academy of Sciences of the USSR

Abstract: For a generalized function which is analytic with respect to some of its variables in the sense of Gording and Malgrange we prove a theorem on representation in the form of a power series in these variables which converges in $D'$ and a corresponding uniqueness theorem. We also obtain necessary and sufficient conditions for a generalized function to be entire with respect to some of its variables.

UDC: 517.5

Received: 30.05.1974

 English version: Mathematical Notes, 1975, 18:3, 785–790

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