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The determination of caloric morphisms on Euclidean domains

Published online by Cambridge University Press:  22 January 2016

Katsunori Shimomura
Katsunori Shimomura*
Affiliation:
Department of Mathematical Sciences, Ibaraki University, Mito, Ibaraki, 310, Japan, shimomur@mito.ipc.ibaraki.ac.jp
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Abstract

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Let D be a domain in ℝm+1 and E be a domain in ℝn+1. A pair of a smooth mapping f : D → E and a smooth positive function ϕ on D is called a caloric morphism if ϕ ˙u o f is a solution of the heat equation in D whenever u is a solution of the heat equation in E. We give the characterization of caloric morphisms, and then give the determination of caloric morphisms. In the case of m < n, there are no caloric morphisms. In the case of m = n, caloric morphisms are generated by the dilation, the rotation, the translation and the Appell transformation. In the case of m > n, under some assumption on f, every caloric morphism is obtained by composing a projection with a direct sum of caloric morphisms of ℝn+1.

Keywords

31B9935K9935A30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 158 , December 2000 , pp. 133 - 166
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

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