On a space of entire functions rapidly decreasing on \mathbb Rⁿ and its Fourier transformation

2014/11/13 by I. Kh. Musin, Musin, I. Kh., Marat Il'darovich Musin +2
Mathematics · #32A15 #42A38 #42B10 #46E10 #46F05 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #math.FA #msc:32A15 #msc:42A38 #msc:42B10 #msc:46E10 #msc:46F05

paper · pdf · doi:10.48550/arxiv.1411.3478

20 pages

arxiv created 2014/11/13 · openalex publication_date 2014/11/13 · arxiv updated 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A space of entire functions of several complex variables rapidly decreasing on \mathbb Rⁿ and such that their growth along i\mathbb Rⁿ 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 Rⁿ and Paley-Wiener type theorem are obtained.

Related

• On a space of entire functions and its Fourier transformation
• On a Fréchet space of entire functions rapidly decreasing on the real line
• Some topics in complex and harmonic analysis, 3
• Extented Paley-Wiener type theorems for the Mellin and Fourier\n transforms on the half-real line
• On a Space of Infinitely Differentiable Functions on an Unbounded Convex Set in \mathbb Rⁿ Admitting Holomorphic Extension in \mathbb Cⁿ and its Dual