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Cauchy and Poisson integrals of ultradistributions. (English) Zbl 0712.46018
The authors define and study the generalized Cauchy and Poisson integrals of ultradistributions of Beurling type ${\cal D}((M\sb p),L\sp s)$ and of Roumieu type ${\cal D}(\{M\sb p\},L\sp s)$ both of which generalize Schwartz distributions ${\cal D}'\sb L$ for appropriate values of s. Thirteen theorems have been proved in this convection. The authors claim that the work contained in the paper under review, may form a foundation for future research concerning a study of holomorphic functions in tubes which are characterised by either pointwise or norm growths, their boundary values, their recovery in terms of generalized integrals including some related properties. A detailed account of the lines on which this can be accomplished, is also given at the end of the paper.
Reviewer: G.L.N.Rao

46F12Integral transforms in distribution spaces
46F15Hyperfunctions, analytic functionals
46F20Distributions and ultradistributions as boundary values of analytic functions
32A07Special domains in ${\Bbb C}^n$ (Reinhardt, Hartogs, circular, tube)
32A10Holomorphic functions (several variables)
32A40Boundary behavior of holomorphic functions (several variables)