A GENERALIZED MAXIMUM PRINCIPLE FOR CONVOLUTION OPERATORS IN BOUNDED REGIONS

Joerg  Reissinger

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A GENERALIZED MAXIMUM PRINCIPLE FOR CONVOLUTION OPERATORS IN BOUNDED REGIONS

机译：有界区卷积算子的广义最大原理。

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摘要

Dealing with the technically motivated concept of convolution operators in bounded regions of 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 ≤ 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.

机译：针对具有潜在的邻近边界条件的R〜N边界区域中卷积算符的技术动机概念，我们将关于N≤2的合适解的存在性和唯一性的先前证明的结果推广到任意N个维度。在此领域中，除了矩形区域的非常特殊的情况之外，还以充分概括的形式获得了实质性的成果。结果也可以看作是所谓k调和函数的广义最大原理，其中k是给定卷积算子的核。

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来源
《Real analysis exchange》 |2013年第2期|353-376|共24页
作者
Joerg Reissinger;
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作者单位

Neunkirchen a. Br., Geissbergweg 6, Germany 91077;

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正文语种 eng
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关键词
convolution integral equations; smoothing operators; boundary value prob-lems; maximum principle; harmonic functions; approximation theory;

机译：卷积积分方程;平滑运算符;边值问题最大原则谐波函数;近似理论;

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1. Generalized Inverses of Convolution Type Operators on Bounded Intervals [J] . A. M. SIMOES WSEAS Transactions on Mathematics . 2014,第Pta2期

机译：有界区间上卷积类型算子的广义逆
2. Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators [J] . Berestycki Henri, Dolcetta Italo Capuzzo, Porretta Alessio, Journal de Mathematiques Pures et Appliquees . 2015,第5期

机译：退化椭圆算子的最大原理和广义本征值
3. Hypercyclicity and Chaotic Character of Generalized Convolution Operators Generated by Gel'fond-Leont'ev Operators [J] . V. E. Kim Mathematical notes . 2009,第5a6期

机译：Gel'fond-Leont'ev算子生成的广义卷积算子的超周期性和混沌特性
4. On the Differences of the Discrete Weak and Strong Maximum Principles for Elliptic Operators [C] . Miklos E. Mincsovics, Tamas L. Horvath International conference on large-scale scientific computing . 2012

机译：椭圆算子的离散弱和最大原理的区别
5. Spectral theory for generalized bounded variation perturbations of orthogonal polynomials and Schrodinger operators. [D] . Lukic, Milivoje. 2011

机译：正交多项式和Schrodinger算子的广义有界变化摄动的谱理论。
6. On a Variational Formula for the Principal Eigenvalue for Operators with Maximum Principle [O] . Monroe D. Donsker, S. R. S. Varadhan 1975

机译：具有最大原理的算子主特征值的变分公式
7. A Dirichlet Problem for Convolution Operators in Bounded Regions [O] . Reissinger J. 1993

机译：边界区域卷积算子的Dirichlet问题
8. On Maximum Principles for Non-hyperbolic Partial Differential Operators [R] . Philip Hartman, Richard Sacksteder 1957

机译：关于非双曲型偏微分算子的最大值原理

A GENERALIZED MAXIMUM PRINCIPLE FOR CONVOLUTION OPERATORS IN BOUNDED REGIONS

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