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A note on the Cauchy Bochner formula for a class of Beurling ultradistributions. (English) Zbl 0713.46026

In a previous paper [Rend. Sem. Math. Univ. Padova 77, 1-13 (1987; Zbl 0636.46043)] the author introduces the space \(D_ 2^{'(M)}\) and in another paper by the author [ibid. 79, 25-36 (1988; Zbl 0663.46036)] he studies the Fourier transformation on \(D_ 2^{'(M)}\). In the present paper the author discusses the generalized Cauchy-Bochner representation for elements of \(D_ 2^{'(M)}\) which, he claims, enables to give a characterization of a family of Hilbert pairs in \(D_ 2^{'(M)}\) with respect to the cone \(R^ q_ f\).
Reviewer: G.L.N.Rao

MSC:

46F12 Integral transforms in distribution spaces
46F15 Hyperfunctions, analytic functionals
46F20 Distributions and ultradistributions as boundary values of analytic functions
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
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