Cauchy-Szegö integrals for systems of harmonic functions
Circulant preconditioners for convolution-like integral equations with higher-order quadrature rules.
Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives
This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...
Continuation of holomorphic solutions to convolution equations in complex domains
For an analytic functional on , we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in . We determine the directions in which every solution can be continued analytically, by using the characteristic set.
Convolution operators on expanding polyhedra: limits of the norms of inverse operators and pseudospectra.
Cooling of a layered plate under mixed conditions.
Cooling of a plate with general boundary conditions.
Dual integral equations -- revisited.
Duality Estimates for the Numerical Solution of Integral Equations.
Eine Klasse von Convolutoren.
Entropy and Eigenvalues of Certain Integral Operators.
Error analysis for the finite element approximation of a radiative transfer model
Estimation of the condition number of a matrix in the direct discretization of the Symm equation on a quasi-uniform grid.
Exponential convergence of hp quadrature for integral operators with Gevrey kernels
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...
Exponential convergence of hp quadrature for integral operators with Gevrey kernels
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...
Extension de fonctions de type positif et entropie associée. Cas multidimensionnel
Faltung hypersingulärer Integraloperatoren.
Fast solution of periodic integral equations by GMRES.
Finite-part singular integral approximations in Hilbert spaces.
First kind integral equations for the numerical solution of the plane Dirichlet problem
We present, in a uniform manner, several integral equations of the first kind for the solution of the two-dimensional interior Dirichlet boundary value problem. We apply a general numerical collocation method to the various equations, and thereby we compare the various integral equations, and recommend two of them. We give a survey of the various numerical methods, and present a simple method for the numerical solution of the recommended integral equations.