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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap105-2-5,
author = {S\l awomir Michalik},
title = {On Borel summable solutions of the multidimensional heat equation},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {167-177},
zbl = {1255.35077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap105-2-5}
}
Sławomir Michalik. On Borel summable solutions of the multidimensional heat equation. Annales Polonici Mathematici, Tome 105 (2012) pp. 167-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap105-2-5/