zbMATH — the first resource for mathematics

Structural properties of the spaces of tempered ultradistributions. (English) Zbl 0795.46028
Dimovski, Ivan et al., Complex analysis and generalized functions. Papers from the fifth international conference on complex analysis and applications and symposium on generalized functions held in Varna, Bulgaria, September 15-21, 1991. Sofia: Publishing House of the Bulgarian Academy. 169-184 (1993).
Summary: We introduce the spaces of tempered ultradistributions of Beurling and Roumieu type by following the approach of H. Komatsu [J. Fac. Sci. Univ. Tokyo, Sect. I A Mat. 20, 25-105 (1973; Zbl 0258.46039)] to the theory of ultradistributions. The first structural theorem and a boundary value representation for the elements of these spaces are given. The Fourier and the Laplace transformations on the spaces of tempered ultradistributions are introduced and analyzed.
For the entire collection see [Zbl 0787.00025].

46F15 Hyperfunctions, analytic functionals
46F12 Integral transforms in distribution spaces
46F20 Distributions and ultradistributions as boundary values of analytic functions