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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Polycaloric Distributions and the Generalized Heat Operator
verfasst von : Viorel Catană
Erschienen in: Pseudo-Differential Operators, Generalized Functions and Asymptotics
Verlag: Springer Basel
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The aim of this paper is to introduce the notion of
p
-caloric distributions with respect to the generalized heat operator and to prove a representation formula. Based on the representation formula for
p
-caloric distributions and using the parametrix of the generalized heat operator we shall give two extensions of Poisson formula. Finally, we shall define the generalized iterated heat operator of order
$$\lambda\,\,\in\,\,\mathrm C,{\rm Re}\, \lambda\,{<}\,{0}$$
by means of the kernel distribution of its parametrix.