MEASURE-COMPACT OPERATORS, ALMOST COMPACT OPERATORS, AND LINEAR FUNCTIONAL EQUATIONS IN L_p

V. B. Korotkov

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MEASURE-COMPACT OPERATORS, ALMOST COMPACT OPERATORS, AND LINEAR FUNCTIONAL EQUATIONS IN L_p

机译：L_p中的紧致算子，几乎紧算子和线性函数方程

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Under study are the measure-compact operators and almost compact operators in L_p. We construct an example of a measure-compact operator that is not almost compact. Introducing two classes of closed linear operators in L_p, we prove that the resolvents of these operators are almost compact or measure-compact. We present methods for the reduction of linear functional equations of the second kind in L_p with almost compact or measure-compact operators to equivalent linear integral equations in L_p with quasidegenerate Carleman kernels.

机译：正在研究的是L_p中的紧致算子和几乎紧致算子。我们构造了一个紧凑紧凑的算子示例。在L_p中引入两类封闭线性算子，我们证明了这些算子的分解几乎是紧凑的或度量紧凑的。我们提出了用近似压缩或度量紧致算子将L_p中的第二种线性泛函方程简化为具有拟边生成Carleman核的L_p中的等效线性积分方程的方法。

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来源
《Siberian Mathematical Journal》 |2013年第3期|共8页
作者
V. B. Korotkov;
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正文语种 eng
中图分类数学;
关键词
almost compact operator; measure-compact operator; integral operator; Carleman operator; linear functional equation of the second kind in L_p; linear integral equations in L_p.;

机译：几乎紧致算子;度量紧算子;积分算子;Carleman算子;L_p中第二类线性函数方程;L_p中线性积分方程。;

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专利

1. MEASURE-COMPACT OPERATORS, ALMOST COMPACT OPERATORS, AND LINEAR FUNCTIONAL EQUATIONS IN L_p [J] . V. B. Korotkov Siberian Mathematical Journal . 2013,第3期

机译：L_p中的紧致算子，几乎紧算子和线性函数方程
2. The Best Approximation of Laplace Operator by Linear Bounded Operators in the Space L_p [J] . A. A. Koshelev Russian mathematics . 2011,第6期

机译：L_p空间中线性有界算子对Laplace算子的最佳逼近
3. Finite-Dimensional Linear Approximations of Solutions to General Irregular Nonlinear Operator Equations and Equations with Quadratic Operators [J] . Kokurin M.Y. Computational mathematics and mathematical physics . 2010,第11期

机译：一般不规则非线性算子方程和带二次算子的方程解的有限维线性近似
4. High-Order Compact-Stencil Summation-By-Parts Operators for the Compressible Navier-Stokes Equations [C] . D. C. Del Rey Fernandez, D. W. Zingg AIAA computational fluid dynamics conference . 2013

机译：可压缩的Navier-Stokes方程的高阶紧凑模具按部分求和
5. Compact operators and the Schroedinger equation [D] . Kazemi, Parimah 2006

机译：紧算子和薛定inger方程
6. Some Linear Operators in the Theory of Partial Differential Equations [O] . S. Bergman, M. Schiffer 1950

机译：偏微分方程理论中的一些线性算子
7. Maximal $L_p$-Regularity and R-sectorial Operators (Nonlinear evolution equations and applications) [O] . Clement Ph. 2001

机译：最大$ L_p $-正则和R部门算子（非线性演化方程和应用）
8. Well-Posedness of Functional Differential Equations with Nonatomic D Operators [R] . Burns, J. A., Herdman, T. L., Turi, J. 1985

机译：具有非原子D算子的泛函微分方程的适定性

MEASURE-COMPACT OPERATORS, ALMOST COMPACT OPERATORS, AND LINEAR FUNCTIONAL EQUATIONS IN L_p

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