On a space of entire functions rapidly decreasing on ${\mathbb R}^n$ and its Fourier transformation

I. Kh. Musin; M. I. Musin

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arXiv · 1411.3478

On a space of entire functions rapidly decreasing on ${\mathbb R}^n$ and its Fourier transformation

I. Kh. Musin·M. I. Musin

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Abstract

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with a help of a family of weight functions is considered in the paper. For this space an equivalent description in terms of estimates on all partial derivatives of functions on ${\mathbb R}^n$ and Paley-Wiener type theorem are obtained.

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I. Kh. Musin, M. I. Musin. 2014-11-13. On a space of entire functions rapidly decreasing on ${\mathbb R}^n$ and its Fourier transformation. https://arxiv.org/abs/1411.3478

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