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Mathematics > Complex Variables

arXiv:1501.02880 (math)
[Submitted on 13 Jan 2015]

Title:On a space of entire functions and its Fourier transformation

Authors:I.Kh. 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 (not radial in general) 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 given.
Comments: Short version of a paper submitted to the journal "`Concrete operators"'
Subjects: Complex Variables (math.CV); Functional Analysis (math.FA)
MSC classes: 32A15, 42B10, 46E10, 46F05, 42A38
Cite as: arXiv:1501.02880 [math.CV]
  (or arXiv:1501.02880v1 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1501.02880

Submission history

From: Ildar Musin Khamitovich [view email]
[v1] Tue, 13 Jan 2015 03:55:07 UTC (6 KB)
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