Toeplitz Operators and Related Topics

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.