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The Appell transform and the semigroup property for temperatures
Published online by Cambridge University Press: 09 April 2009
Abstract
We prove that if u(x, t) is a solution of the one dimensional heat equation and if A u(x, t) is its Appell transform, then u(x, t) has the semi-group (Huygens) property in a domain D if and only if A u(x, t) has the semi-group property in a dual region. We apply this result to simplify and extend some results of Rosenbloom and Widder.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 60 , Issue 1 , February 1996 , pp. 109 - 117
- Copyright
- Copyright © Australian Mathematical Society 1996
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