An integral transformation and its applications to harmonic analysis on the space of solutions of heat equation
type: Item
instance of: scholarly article
title: An integral transformation and its applications to harmonic analysis on the space of solutions of heat equation
zbMATH Open document ID: 0948.35060
author: Soon-Yeong Chung
author: Yongjin Yeom
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2000-11-19T00:00:00Z
review text: Summary: We introduce an integral transformation \(T\) defined by \[ (Tf)(x,t)= \int e^{-ixy-t |y|2}f(y)dy, \quad f\in L^1(\mathbb{R}^n) \] in order to do harmonic analysis on the space of \(C^\infty\)-solutions of the heat equation. First, the Paley-Wiener type theorem for the transformation \(T\) will be given for the \(C^\infty\)-functions and distributions with compact support. Secondly, as an application of the transformation the solutions of the heat equation given on the torus \(T^n\) will be characterized. Finally, we represent solutions of heat equation as an infinite series of Hermite temperatures, which are to be defined as the images of Hermite polynomials under the transformation \(T\).
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 35A22
zbMATH DE Number: 1455563
zbMATH Keywords: Paley-Wiener type theorem
zbMATH Keywords: infinite series of Hermite temperatures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195143421
OpenAlex ID: W2084543365
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DOI: 10.2977/PRIMS/1195143421
description: scientific article; zbMATH DE number 1455563