This volume is dedicated to Harold Widom, a distinguished mathematician and renowned expert in the area of Toeplitz, Wiener-Hopf and pseudodifferential operators, on the occasion of his sixtieth birthday. The book opens with biographical material and a list of the mathematician's publications, this being followed by two papers based on Toeplitz lectures which he delivered at Tel Aviv University in March, 1993. The rest of the book consists of a selection of papers containing some recent achievements in the following areas: Szegö-Widom asymptotic formulas for determinants of finite sections of Toeplitz matrices and their generalizations, the Fisher-Hartwig conjecture, random matrices, analysis of kernels of Toeplitz matrices, projectional methods and eigenvalue distribution for Toeplitz matrices, the Fredholm theory for convolution type operators, the Nehari interpolation problem with generalizations and applications, and Toeplitz-Hausdorff type theorems. The book will appeal to a wide audience of pure and applied mathematicians.

Inhalt

Eigenvalue distribution for nonselfadjoint Toeplitz matrices.- Random Hermitian matrices and (nonrandom) Toeplitz matrices.- The extended Fisher-Hartwig conjecture for symbols with multiple jump discontinuities.- A relative Toeplitz-Hausdorff theorem.- Operator-valued Szegö-Widom limit theorems.- The Adamjan-Arov-Krein theorem in general and regular representations of ?2 and the symplectic plane.- Projection method for block Toeplitz operators with operator-valued symbols.- Szegö-Widom-type limit theorems.- (Semi)-Fredholmness of convolution operators on the spaces of Bessel potentials.- Kernels of Toeplitz operators.- A fixed point approach to Nehari's problem and its applications.