In the numerical evaluation of geodetic convolution integrals, whether by quadrature or discrete/fast Fourier transform (D/FFT) techniques, the integration kernel is sometimes computed at the centre of the discretised grid cells. For singular kernels a common case in physical geodesy this approximation produces significant errors near the computation point, where the kernel changes rapidly acro...

Debbah and Ryan have recently [DR07] proved a result about the limit empirical singular distribution of the sum of two rectangular random matrices whose dimensions tend to infinity. In this paper, we reformulate it in terms of the rectangular free convolution introduced in [BG07b] and then we give a new, shorter, proof of this result under weaker hypothesis: we do not suppose the probability me...

In this paper, we connect rectangular free probability theory and spherical integrals. In this way, we prove the analogue, for rectangular or square non symmetric real matrices, of a result that Guionnet and Mäıda proved for symmetric matrices in [GM05]. More specifically, we study the limit, as n,m tend to infinity, of 1 n logE{exp[nmθXn]}, where Xn is an entry of UnMnVm, θ ∈ R, Mn is a certai...

Convolution type Calderr on-Zygmund singular integral operators with rough kernels p.v. (x)=jxj n are studied. A condition on implying that the corresponding singular integrals and maximal singular integrals map L p ! L p for 1 < p < 1 is obtained. This condition is shown to be diierent from the condition 2 H 1 (S n?1).

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...