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Extension of infinitely differentiable functions to entire functions with consistent growth estimates and Paley-Wiener-Schwartz type theorems. (Russian) Zbl 1096.46508

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
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