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.
Citation
Jörg Reißinger. "A Generalized Maximum Principle for Convolution Operators in Bounded Regions." Real Anal. Exchange 38 (2) 353 - 376, 2012/2013.
Information