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On the $A$-integrability of singular integral transforms [PDF]
Annales de l’institut Fourier, 1984 openaire +2 more sources
A note on the singular integral
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1937 openaire +3 more sources
Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms
Open Mathematics, 2014 Osękowski Adam
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Product Integration for Singular Integrals and Singular Integral Equations
1979Integral equations with weakly singular kernels often have solutions which have derivative singularities at the end points of the range of integration. The error analysis of a product integration method for such integral equations depends on the error analysis of the product integration method applied to integrals of the form \(\int\limits_0^1 {g\left(
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2011
§ 1. In these lectures I present some of the results obtained jointly with A. P. Calderon during the last few years. Not all the results stated here are accompanied by proofs, and for additional details the reader is referred to original papers (**).
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§ 1. In these lectures I present some of the results obtained jointly with A. P. Calderon during the last few years. Not all the results stated here are accompanied by proofs, and for additional details the reader is referred to original papers (**).
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Singular Series and Singular Integrals
1991For a given \(\wp \), let p be the rational prime contained in \(\wp \), and let b, e, f denote the integers such that $$ {\wp ^e}\parallel p, {\text{ }}{p^b}\parallel k{\text{ }}\operatorname{and} {\text{ }}N\left( \wp \right) = {p^f}. $$
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Singular Integral Equations [PDF]
, 1989 In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the ...
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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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1971
Publisher Summary An integral equation is called singular if either the range of integration is infinite or the kernel has singularities within the range of integration. Such equations occur rather frequently in mathematical physics and possess very unusual properties.
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Publisher Summary An integral equation is called singular if either the range of integration is infinite or the kernel has singularities within the range of integration. Such equations occur rather frequently in mathematical physics and possess very unusual properties.
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Minkowski content and singular integrals
Chaos, Solitons & Fractals, 2003Assume that lower and upper d-dimensional Minkowski contents of are different both from 0 and . We show that the function d(x, A)- is integrable in a tubular neighbourhood of A if and only if
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