Convolution type operators on cones and their finite sections

Abstract

AbstractThis paper is concerned with finite sections of convolution type operators defined on cones, whose symbol is the Fourier transform of an integrable function on ℝ2. The algebra of these finite sections satisfies a set of axioms (standard model) that ensures some asymptotic properties like the convergence of the condition numbers, singular values, ε‐pseudospectrum and also gives a relation between the singular values of an approximation sequence and the kernel dimensions of a set of associated operators. This approach furnishes a method to determine whether a Fredholm convolution operator on a cone is invertible. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)