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 60th 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: Szego-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, Fredholm theory for convolution type operators, the Nehari interpolation problem with generalizations and applications, and Toeplitz-Hausdorf type theorems. The book should appeal to a wide audience of pure and applied mathematicians.

Table of Contents:
Biography of H. Widom, E.L. Basor and E.M. Landesman; to Harold Widom on his 60th birthday, I. Kaplansky; Harold Widom's publications; eigenvalue distribution for nonselfadjoint Toeplitz matrices, H. Widom; random Hermitian matrices and (nonrandom) Toeplitz matrices, H. Widom; the extended Fisher-Hartwig conjecture for symbols with multiple jump discontinuities - some special cases, references, E.L. Basor and K.E. Morrison; a relative Toeplitz-Hausdorff theorem, H. Bercovici et al; operator-valued Szego-Widom limit theorems - Toeplitz and Hankel operators with operator-valued symbols, finite section method, the first Szego-Widom limit theorem, the strong Szego-Widom limit theorem, continuous symbols, references, A. Boettcher and B. Silbermann; the Adamjan-Arov-Krein theorem in general and regular representations of R(2) and the symplectic plane - Hankel forms in discrete and continuous evolution systems, the A-A-K theorem in general and regular representations of R, the A-A-K theorem for general representations of R(2) and (R(2),[,]), A-A-K theorems in the regular representation of R(2), the A-A-K theorem in the regular representation of the symplectic plane, references, M. Cotlar and C. Sadosky; projection method for block Toeplitz operators with operator-valued symbols - projection method for compressions, applications of block Toeplitz operators with operator-valued symbols, projection method with two directions, the projection method for block pair operators, the theorem for the non-Toeplitz case, references, I. Gohberg and M.A. Kaashoek; Szego-Widom-type limit theorems - the main results, illustrative examples, proofs of theorems 2.1, 2.2, references, I. Gohberg and N Krupnik; (semi)-Fredholmness of convolution operators on the spaces of Bessel potentials - main results, auxiliary results, invertibility and factorability of local representatives, references, Y. Krlovich and I. Spitovsky; kernels of Toeplitz operators - De Branges-Rovnyak spaces, Hitt's theorem, Hayashi's theorem, rigid functions, references, D. Sarason; a fixed point approach to Nehari's problem and its applications - abstract Nehari's theorem, main examples and corollaries, Iokhvidov-Ky Fan theorem and some of its applications - a generalized AAK theorem, proof of the generalized Nehari's theorem, proof of the Iokhvidov-Ky Fan theorem, references, S. Treil and A. Volberg.