Real Analysis Exchange

A Generalized Maximum Principle for Convolution Operators in Bounded Regions

Jörg Reißinger

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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

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894897

Mathematical Reviews number (MathSciNet)
MR3261882

Zentralblatt MATH identifier
1297.47028

Subjects
Primary: 26E40: Constructive real analysis [See also 03F60] 54C30: Real-valued functions [See also 26-XX]
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 54C08: Weak and generalized continuity

Keywords
convolution integral equations smoothing operators boundary value problems maximum principle harmonic functions approximation theory

Citation

Reißinger, Jörg. A Generalized Maximum Principle for Convolution Operators in Bounded Regions. Real Anal. Exchange 38 (2012), no. 2, 353--376. https://projecteuclid.org/euclid.rae/1403894897


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