Summable solutions of some partial differential equations and generalised integral means

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Michalik, Slawomir¹ 

[1] Cardinal Stefan Wyszynski Univ, Coll Sci, Fac Math & Nat Sci, Woycickiego 1-3, PL-01938 Warsaw, Poland

关键词: k-Summability;    Formal power series;    Linear partial differential equations;    Generalised integral means;    Pizzetti's formula;   

DOI  :  10.1016/j.jmaa.2016.07.031

来源: Elsevier

【 摘 要 】

We describe partial differential operators for which we can construct generalised integral means satisfying Pizzetti-type formulas. Using these formulas we give a new characterisation of summability of formal power series solutions to some multidimensional partial differential equations in terms of holomorphic properties of generalised integral means of the Cauchy data. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free