Geodesic
On Borel summable solutions of the multidimensional heat equation
Sławomir Michalik1
1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21, Śniadeckich 8 00-956 Warszawa, Poland and Faculty of Mathematics and Natural Sciences College of Science Cardinal Stefan Wyszyński University Wóycickiego 1/3 01-938 Warszawa, Poland
Annales Polonici Mathematici, Tome 105 (2012) no. 2, pp. 167-177.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give a new characterisation of Borel summability of formal power series solutions to the $n$-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.
DOI : 10.4064/ap105-2-5
Keywords: characterisation borel summability formal power series solutions n dimensional heat equation terms holomorphic properties integral means cauchy derive borel sum summable formal solutions

Sławomir Michalik 1

1 Institute of Mathematics Polish Academy of Sciences P.O. Box 21, Śniadeckich 8 00-956 Warszawa, Poland and Faculty of Mathematics and Natural Sciences College of Science Cardinal Stefan Wyszyński University Wóycickiego 1/3 01-938 Warszawa, Poland 
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Sławomir Michalik. On Borel summable solutions of the
 multidimensional heat equation. Annales Polonici Mathematici, Tome 105 (2012) no. 2, pp. 167-177. doi : 10.4064/ap105-2-5. http://geodesic.mathdoc.fr/articles/10.4064/ap105-2-5/

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