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

2013/01/10 by Marat Il'darovich Musin, Musin, Marat
Mathematics · #42A38 (Primary) 30D15 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1301.2037

openalex publication_date 2013/01/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A weighted space of entire functions rapidly decreasing on the real line is considered in the paper. A growth of these functions along the imaginary axis is controlled by some system of weight functions. The Fourier transform of functions of this space is studied. Equivalent description of the considered space in terms of estimates on derivatives of functions on real line is obtained.

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