Algebraic and differential properties of polynomial Fourier transformation
type: Item
instance of: scholarly article
title: Algebraic and differential properties of polynomial Fourier transformation
zbMATH Open document ID: 1452.46032
published in: Matematychni Studiï
publication date: 2020-04-23T00:00:00Z
review text: The main result of the paper formulated in Theorem~6 deals with the generalized polynomial Fourier transformation. Namely, the convolution theorem is proved for the case of the polynomial Fourier transformation. Moreover, classical results related to differentiation of generalized (in the Sobolev-Schwartz sense) functions are extended to the case of the generalized polynomial Fourier transformation. Finally, Theorem~7 demonstrates that the generalized polynomial Fourier transformation acts as a homomorphism of appropriate algebras.
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46F25
Mathematics Subject Classification ID: 46E50
zbMATH DE Number: 7192746
zbMATH Keywords: polynomials on infinite-dimensional spaces
zbMATH Keywords: rapidly decreasing functions
zbMATH Keywords: Schwartz distributions
zbMATH Keywords: Fourier transformation
author: Sergii Sharyn
reviewed by: Denis Sidorov
MaRDI profile type: Publication
full work available at URL: ms.53.1.59-68
OpenAlex ID: W3010983518
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DOI: 10.30970/MS.53.1.59-68
description: scientific article; zbMATH DE number 7192746