## Real Analysis Exchange

### A Generalized Maximum Principle for Convolution Operators in Bounded Regions

Jörg Reißinger

#### Abstract

Dealing with the technically motivated concept of convolution operators in bounded regions of $\mathbb{R}^{N}$ with an underlying nearby boundary condition we extend a formerly proved result about the existence and uniqueness of suitable solutions for dimension $N\leq 2$ to arbitrary dimensions $N$. Thus, a first substantial result in a sufficiently generalized form, beyond the very specific case of rectangular regions, is established in this field. The result can also be seen as a generalized maximum principle for so called $k$-harmonic functions where $k$ is the kernel of the given convolution operator.

#### Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 353-376.

Dates
First available in Project Euclid: 27 June 2014