Results 311 to 320 of about 248,172 (367)
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2011
Algebras generated by singular integral operators and convolution operators are one of the numerous instances where local principles and projection theorems have been successfully applied. And conversely, it was mainly the study of these algebras which stimulated the development of local principles and projection theorems as a tool in operator theory ...
Steffen Roch +2 more
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Algebras generated by singular integral operators and convolution operators are one of the numerous instances where local principles and projection theorems have been successfully applied. And conversely, it was mainly the study of these algebras which stimulated the development of local principles and projection theorems as a tool in operator theory ...
Steffen Roch +2 more
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Acta Mathematica Scientia, 1998
Abstract In this paper, the author discusses some singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, and obtain some useful properties for them. These results improve both the classical theory of singular integral equation and the classical theory of ...
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Abstract In this paper, the author discusses some singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, and obtain some useful properties for them. These results improve both the classical theory of singular integral equation and the classical theory of ...
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Eigenvalues of Weakly Singular Integral Operators
Journal of the London Mathematical Society, 1990We determine the asymptotic order of decay of eigenvalues of weakly singular integral operators, i.e. operators defined by kernels of the form \[ K(x,y)=\frac{L(x,y)(1+| \log \| x-y\| |)^{\gamma}}{\| x-y\|^{N(1-\alpha)}};\quad x,y\in \Omega.
Cobos, Fernando, Kühn, Thomas
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Singular integral operators and spherical harmonics
Transactions of the American Mathematical Society, 1956where the "characteristic function" k(o) is, say, continuous on the unit sphere and its integral vanishes there. In this paper I shall consider the operation (1) as the convolution of f with a distribution K in the sense of Laurent Schwartz, as it has been done already for n=1 by Schwartz himself [17, p. 115].
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Singular Integral Operators on Besov Spaces
Mathematische Nachrichten, 1988AbstractSummary. We introduce generalized BESOV spaces in terms of mean oscillation and weight functions, following a recent work of Dorronsoro, and study the continuity of singular integral operators on them. Relations between these spaces and the BESOV spaces in terms of modulus of continuity are also studied.
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Two problems about singular integral operator
Approximation Theory and its Applications, 1991Let \(\alpha_ 1,\dots,\alpha_ n\) be given real numbers such that \(\alpha_ j\geq 1\) for all \(1\leq j\leq n\), and let \(\delta_ t=\exp(A\ln t)\) (\(t>0\)), where \(A=\text{diag}\{\alpha_ 1,\dots,\alpha_ n\}\). Let \(\rho(x)\) be the unique positive number satisfying \(\delta_{\rho(x)^{-1}}x\in\Sigma^{n-1}=\bigl\{x:\;\sum_{i=1}^ n \alpha_ i^{-1} x_ i^
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2001
We present in this chapter the definition and the main properties of the singular integral operator. These results are quite classical and were first studied by Giraud [78] in France and then Calderon and Zygmund in the United States and Michlin in Russia. The present exposition uses some ideas of the notes of V. Neri and the book of E.M.
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We present in this chapter the definition and the main properties of the singular integral operator. These results are quite classical and were first studied by Giraud [78] in France and then Calderon and Zygmund in the United States and Michlin in Russia. The present exposition uses some ideas of the notes of V. Neri and the book of E.M.
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Compactness for the commutators of multilinear singular integral operators with non-smooth kernels
Applied Mathematics-A Journal of Chinese Universities, 2014In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered.
Rui Bu, Jiecheng Chen
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1999
In this paper, we discuss some singular integral operators and singular quadrature operators for singular integral equations with Hilbert kernel, and obtain some useful properties of them. These results improve both the classical theory of singular integral equation with Hilbert kernel and the classical theory of singular quadrature with Hilbert kernel.
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In this paper, we discuss some singular integral operators and singular quadrature operators for singular integral equations with Hilbert kernel, and obtain some useful properties of them. These results improve both the classical theory of singular integral equation with Hilbert kernel and the classical theory of singular quadrature with Hilbert kernel.
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On a singular integral operator
Russian Mathematical Surveys, 1988Let D(\(\subset {\mathbb{C}})\) be a bounded domain with the smooth boundary. The authors consider an operator of the form \(A=a(z)I+b(z)K+c(z)S+d(z)KS\) acting in the space \(L^ p(D ...
Bojmatov, K. Kh., Dzhangibekov, G.
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