Results 111 to 120 of about 186 (123)
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Approximation of Hypersingular Integral Operators With Cauchy Kernel
Numerical Functional Analysis and Optimization, 2016ABSTRACTIn the present article, the hypersingular integral operator with Cauchy kernel H is approximated by a sequence of operators of a special form, and it is proved that the approximating operators Hn strongly converge to the operator H and for an algebraic polynomial of degree not higher than n the operators Hn and H coincide.
Rashid A. Aliev, Chinara A. Gadjieva
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Rough hypersingular integral operators with an oscillating factor
Applied Mathematics-A Journal of Chinese Universities, 2006Let \(n\geq 2\) and \(S^{n-1}\) be the unit sphere in \({\mathbb R}^n\). Let \(H^r(S^{n-1})\) be the Hardy spaces on \(S^{n-1}\). For a smooth function \(f\) on \({\mathbb R}^n\), we write \(f_{(x,s)}(y')=f(x-|y|y')\), where \(y'=y/|y|\) and \(s=|y|\).
Chen, Jiecheng, You, Ying
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Numerical evaluation of certain hypersingular integrals using refinable operators
Mathematics and Computers in Simulation, 2011The authors consider the problem of numerically computing the Hadamard finite-part integral \(\int_{-1}^1 u(t) (t-\lambda)^{-p} dt\) with \(\lambda \in (-1,1)\) and \(p \in \{1,2,3,\ldots\}\). The algorithm is based on the classical and well known principle of subtracting the singularity.
GORI L, PELLEGRINO, ENZA, SANTI E.
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Hypersingular integral operators along surfaces
Integral Equations and Operator Theory, 2002In this paper, the author obtains the boundedness of certain singular integral operators along curves and surfaces with highly singular kernels. In the lower-dimensional case, the author studies the operator \[ Tf(u,v)= \text{p.v. }\int f(u-y, v-\gamma(y)) e^{i|y|^{-\beta}} y^{-1}|y|^{-\alpha} h(y) dy, \] where \(u,v,y\in \mathbb{R}\), \(h\) is a ...
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Partial radiation conditions and hypersingular integral operators
Computational Mathematics and Mathematical Physics, 2009Summary: The structure of partial radiation conditions is analyzed. It is found that the principal part of the operator defining these conditions defines a hypersingular operator. The series corresponding to the operator associated with the boundary conditions is transformed to a rapidly converging series.
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Computer Methods in Applied Mechanics and Engineering, 1992
The authors present comparative applications of the collocation boundary element method and the variational method to the solution of the three- dimensional thin shell acoustic problem. In the boundary integral formulation of this problem a hypersingular integral operator appears that makes the implementation of the collocation method difficult.
Jeans, R., Mathews, I. C.
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The authors present comparative applications of the collocation boundary element method and the variational method to the solution of the three- dimensional thin shell acoustic problem. In the boundary integral formulation of this problem a hypersingular integral operator appears that makes the implementation of the collocation method difficult.
Jeans, R., Mathews, I. C.
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Hypersingular integral operators in diffraction problems of electromagnetic waves on open surfaces
Computational Mathematics and Modeling, 1994The three-dimensional problem of diffraction of a monochromatic electromagnetic field on an open ideally conducting surface has been reduced in [1] to the solution of an integrodifferential equation for the induced density of surface currents. In [2] this equation has been represented in hypersingular form, with the divergent integral understood in the
Zakharov, E. V., Khaleeva, I. V.
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A rough hypersingular integral operator with an oscillating factor on function space
Applied Mathematics-A Journal of Chinese Universities, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fractional Powers of Operators Via Hypersingular Integrals
2000The well known Balakrishnan formula represents the fractional power (–A) α in case of the generator A of a semigroup T t , t > 0, in terms of a (hyper)-singular integral with respect to the variable t ∈ R + 1 that is $${{( - A)}^{\alpha }}f = \frac{1}{{\Gamma ( - \alpha )}}\int_{0}^{\infty } {{{t}^{{ - \alpha - 1}}}} ({{T}_{t}} - I)fdt,$$ where ...
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Numerische Mathematik, 1998
The aim of this paper is to investigate preconditioners for the stiffness matrix of a linear system, which provide good bounds for the spectral condition number \(k\). The study of the preconditioners is based on domain decomposition. As a model problem the weak form of the hypersingular integral equation \[ \langle Du,v\rangle _{L^{2}(\Gamma)}=\langle
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The aim of this paper is to investigate preconditioners for the stiffness matrix of a linear system, which provide good bounds for the spectral condition number \(k\). The study of the preconditioners is based on domain decomposition. As a model problem the weak form of the hypersingular integral equation \[ \langle Du,v\rangle _{L^{2}(\Gamma)}=\langle
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