On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree -n

O. G. Avsyankin; N. K. Karapetyants

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On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree -n

机译：具有n次齐次核的多维积分算子的伪谱

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摘要

We study the limit behavior of the spectral characteristics of truncated multidimensional integral operators whose kernels are homogeneous of degree -n and invariant under the rotation group SO(n). We prove that the limit of the ε-pseudospectra of the truncated operators K_τ as τ → 0 is equal to the union of the ε-pseudospectra of the original operator K and the "transposed" operator K-tilde.

机译：我们研究了旋转群SO（n）下截断的多维积分算子的频谱特性的极限行为，该算子的核是度为n且是不变的。我们证明截断算子K_τ的ε-伪谱的极限为τ→0等于原始算子K和“转置”算子K-tilde的ε-伪谱的并集。

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《Siberian Mathematical Journal》 |2003年第6期|共16页
作者
O. G. Avsyankin; N. K. Karapetyants;
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正文语种 eng
中图分类数学;
关键词
multidimensional integral operator; homogeneous kernel; spectrum; pseudospectrum; truncated operator;

机译：多维积分算子;齐次核;谱;伪谱;截断算子;

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专利

1. On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree -n [J] . O. G. Avsyankin, N. K. Karapetyants Siberian Mathematical Journal . 2003,第6期

机译：具有n次齐次核的多维积分算子的伪谱
2. SOME SHARP INEQUALITIES FOR MULTIDIMENSIONAL INTEGRAL OPERATORS WITH HOMOGENEOUS KERNEL: AN OVERVIEW AND NEW RESULTS [J] . Lukkassen D., Persson L. -E., Samko S. G., Mathematical inequalities & applications . 2016,第2期

机译：具有均质核的多维积分算子的一些尖锐不等式：概述和新结果
3. Multidimensional integral operators with homogeneous kernels and with coefficients oscillating at infinity [J] . Avsyankin O. G. Differential equations: A translation of differensial'nye uraveniya . 2015,第9期

机译：具有齐次核且系数在无穷大处振荡的多维积分算子
4. Boundedness and Invertibility of Multidimensional Integral Operators with Anisotropically Homogeneous Kernels in Weighted Lp–spaces [C] . Miroshnikova Elena International Conference on Mathematical Problems in Engineering and Aerospace Sciences . 2014

机译：多维积分算子在加权LP空间中具有各向异性均质核的多维积分算子可逆性
5. On homogeneous Calderon-Zygmund operators with rough kernels (Calderon-Zygmund operators, Singular integrals). [D] . Stefanov, Atanas Gueorguiev. 1999

机译：在具有粗糙核的齐次Calderon-Zygmund算子上（Calderon-Zygmund算子，奇异积分）。
6. Equivalent conditions and applications of a class of Hilbert-type integral inequalities involving multiple functions with quasi-homogeneous kernels [O] . Junfei Cao, Bing He, Yong Hong, -1

机译：一类涉及具有齐齐核的多重函数的希尔伯特型积分不等式的等价条件和应用
7. Some sharp inequalities for multidimensional integral operators with homogeneous kernel: an overview and new results [O] . Dag Lukkassen, Lars-Erik Persson, Stefan Samko, 2016

机译：多维积分运算符与同质内核的一些尖锐不等式：概述和新结果

On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree -n

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