Certain classes of analytic functions and distributions with general exponential growth

Byung Keun Sohn

doi:10.4134/BKMS.2014.51.6.1805

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Bull. Korean Math. Soc. 2014; 51(6): 1805-1827

Printed November 30, 2014

https://doi.org/10.4134/BKMS.2014.51.6.1805

Certain classes of analytic functions and distributions with general exponential growth

Byung Keun Sohn

Inje University

Abstract

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Abstract

Let {\kmp} be the generalized tempered distributions of $e^{M(t)}$-growth, where the function $M(t)$ grows faster than any linear functions as $|t| \rightarrow \infty$, and let {\bkmp} be the Fourier transform spaces of {\kmp}. We obtain the relationship between certain classes of analytic functions in tubes, {\kmp} and {\bkmp}.

Keywords: analytic functions, distributions

MSC numbers: 46F20, 46F12, 46F10