Fourier ultrahyperfunctions

V. V. Zharinov

Izvestiya. Mathematics , Tome 16 (1981) no. 3, pp. 479-511.

Résumé

This article is devoted to a systematic study of one class of analytic functionals, called the Fourier ultrahyperfunctions. Distributive lattices of subspaces of Fourier ultrahyperfunctions are determined, and the Fourier and Laplace transforms as well as multipliers and convolutors are described. For a suitable class of analytic functions the concept of the boundary value is introduced, and a theorem of the type of Bogolyubov's "edge-of-the-wedge" theorem is established. Bibliography: 21 titles.

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