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


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.


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


Published: 2012/2013
First available in Project Euclid: 27 June 2014

zbMATH: 1297.47028
MathSciNet: MR3261882

Primary: 26E40 , ‎54C30
Secondary: 26A15 , 54C08

Keywords: approximation theory , boundary value problems , convolution integral equations , Harmonic functions , maximum principle , smoothing operators

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 2 • 2012/2013
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