Results 31 to 40 of about 888,164 (293)
Efficient algorithms for integrals with highly oscillatory Hankel kernels
Results in Applied Mathematics, 2022 We present an efficient numerical algorithm for approximating integrals with highly oscillatory Hankel kernels. First, using the integral expression of the Hankel function, the integral is transformed into the integral of the trigonometric kernel, and ...
Qinghua Wu, Mengjun Sun
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Advanced Engineering Research, 2014 The authors have previously studied two - dimensional Fredholm integral operators with homogeneous kernels of fiber - singular type. For this class of operators, the symbolic calculus is built using the theory of biloc al operators by V.
Vladimir Mikhaylovich Deundyak +1 more
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New estimates for the maximal singular integral [PDF]
, 2009 In this paper we pursue the study of the problem of controlling the maximal singular integral $T^{*}f$ by the singular integral $Tf$. Here $T$ is a smooth homogeneous Calder\'on-Zygmund singular integral of convolution type.
Centre de Recerca Matemàtica +4 more
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Approximation of the Hilbert transform in the Lebesgue spaces
Journal of Numerical Analysis and Approximation Theory, 2023 The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the ...
Rashid Aliev, Lale Alizade
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Rank one perturbations and singular integral operators [PDF]
, 2008 We consider rank one perturbations $A_\alpha=A+\alpha(\cdot,\varphi)\varphi$ of a self-adjoint operator $A$ with cyclic vector $\varphi\in\mathcal H_{-1}(A)$ on a Hilbert space $\mathcal H$. The spectral representation of the perturbed operator $A_\alpha$
Liaw, Constanze, Treil, Sergei
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Solutions of singular integral equations
International Journal of Mathematics and Mathematical Sciences, 1982 Qualitative behavior of solutions of possibly singluar integral equations is studied. It includes properties such as positivity, boundedness and monotonicity of the solutions of the infinite interval.
Rina Ling
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Integrable cross-field generation based on imposed singularity configuration -- the 2D manifold case -- [PDF]
arXiv, 2022 This work presents the mathematical foundations for the generation of integrable cross-field on 2D manifolds based on user-imposed singularity configuration. In this paper, we either use singularities that appear naturally, e.g., by solving a non-linear problem, or use as an input user-defined singularity pattern, possibly with high valence ...
arxiv
Regularity of the minimiser of one-dimensional interaction energies
, 2019 We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind of Fredholm type. Our setting covers applications to dislocation pile-ups,
Kimura, M., van Meurs, P.
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Numerical solution of integral equations with finite part integrals
International Journal of Mathematics and Mathematical Sciences, 1999 We obtain convergence rates for several algorithms that solve a class of Hadamard singular integral equations using the general theory of approximations for unbounded operators.
Samir A. Ashour
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, 2012 In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth deformations of the ...
Costabel, Martin +1 more
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