We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank matrices at an exponential rate in the block rank. We cover in particular the data-space format of H-matrices. We show the approximability result for two types of discretizations. The first one is a saddl...

This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set. Moreover the associated flow appears in two important applications: dislocation dynamics and phasefield theory for fractional reaction-diffusion equations. It is defined by using the level set method. The main results of...

We study the multiplicative Schwarz method for the p-version Galerkin boundary element method for a hypersingular and a weakly singular integral equation of the rst kind and for the h-version for a hypersingular integral equation of the rst kind. We prove that the rate of convergence of the multiplicative Schwarz operator is strictly less than 1 for the h-version for both two level and multilev...

let a(p) denote the class of functions which are analytic in the open unit disk u. by making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

in this paper , numerical solotion of abel's integral equationby using the taylor expanssion of the unknown functionvia collection method based on sinc is considered...

We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...

On logρ(AX)dX ≥ Cn log ‖A‖, where ‖A‖ denotes the operator norm of A (which equals the largest singular value of A), ρ denotes the spectral radius, and the integral is with respect to the Haar measure on On. The same result (with essentially the same proof) holds for the unitary group Un in place of the orthogonal group. The result does not hold in dimension 2.This answers questions asked in [3...