This article is cited in 1 paper

On a space of entire functions decreasing rapidly on a real line

M. I. Musin

Bashkir State University, Ufa, Russia

Abstract: A space of entire functions decreasing rapidly on a real line is introduced. It contains the space of the Fourier–Laplace transforms of infinitely differentiable functions on a real line with a compact support as a proper subspace. The Fourier–Laplace transform of functions of this space is studied. Equivalent description in terms of estimates of derivatives of functions on a real line is obtained for the considered space.

Keywords: the Fourier–Laplace transform, entire functions, Paley–Wiener type theorem.

UDC: 517.982.3

Received: 02.09.2011