Pilipović, S. A note on the Cauchy Bochner formula for a class of Beurling ultradistributions. (English) Zbl 0713.46026 Port. Math. 46, No. 4, 351-359 (1989). 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.) Keywords:Beurling ultradistributions; Cauchy kernels; generalized Cauchy-Bochner representation Citations:Zbl 0636.46043; Zbl 0663.46036 PDFBibTeX XMLCite \textit{S. Pilipović}, Port. Math. 46, No. 4, 351--359 (1989; Zbl 0713.46026) Full Text: EuDML