Abanin, A. V.; Nalbandyan, Yu. S.; Shabarshina, I. S. Extension of infinitely differentiable functions to entire functions with consistent growth estimates and Paley-Wiener-Schwartz type theorems. (Russian) Zbl 1096.46508 Vladikavkaz. Mat. Zh. 6, No. 2, 3-9 (2004). Summary: Interrelations are under study between growth estimates of entire functions in \(\mathbb C^N\) and those of all successive derivatives of their restrictions onto \(\mathbb R^N\). The results obtained are used for proving new Paley-Wiener-Schwartz type theorems for ultradistributions whose supports lie in convex compacta symmetric with respect to all coordinate hyperplanes in \(\mathbb R^N\). MSC: 46F12 Integral transforms in distribution spaces 47G30 Pseudodifferential operators 46F05 Topological linear spaces of test functions, distributions and ultradistributions Keywords:Fourier transform; hyperfunction PDFBibTeX XMLCite \textit{A. V. Abanin} et al., Vladikavkaz. Mat. Zh. 6, No. 2, 3--9 (2004; Zbl 1096.46508) Full Text: EMIS