Branges, L. de (ed.)
Gohberg, I. (ed.)
Rovnyak, J. (ed.)
|Title||Topics in Operator Theory, Ernst D. Hellinger Memorial Volume|
|Year of publication||1990|
|Reviewed by||Michal Zajac|
This is a volume honoring Ernst Hellinger (1883-1950). In a very interesting introductory paper James Rovnyak describes the life and work of Ernst Hellinger. Hellinger's sister Hanna Meissner contributed a nice article entitled "How I, at age 92, remember my brother, 38 years after his death."
The volume contains 19 papers on various topics in Operator theory:
J. Agler: On the representation of certain holomorphic functions defined on a polydisc.
J. Arazy, D. Fisher: Invariant Hilbert spaces of analytic functions on bounded symmetric domains.
J.A. Ball, T.R. Fanney: Closability of differential operators and real subjordan operators.
A. Ben-Artzi, I. Gohberg, M.A. Kaashoek: Invertibility and dichotomy of singular difference equations.
H. Bercovici: On the iterates of a completely nonunitary contraction.
A. Bötcher, S. Roch, B. Silbermann, I.M. Spitkovskii: A Gohberg-Krupnik-Sarason symbol calculus for algebras of Toeplitz, Hankel, Cauchy and Carleman operators.
D.N. Clark: Perturbation and similarity of Toeplitz operators.
T. Constantinescu: Factorization of positive-definite kernels.
A. Dijksma, H. Langer, H. De Snoo: Generalized coresolvents of standard isometric operators and generalized resolvents of standard symmetric relations in Krein spaces.
A. Ghondea: On the structure of linear contractions with respect to fundamental decompositions.
T. Jech: Local topology and spectral theorem.
T.L. Kriete III: Isometries from the Laguerre shift.
H. Langer, R. Mennicken, M. Möller: A second order differential operator depending nonlinearly on the eigenvalue parameter.
D. Sarason: Exposed points in H1, II.
Yu.L. Shmul'yan: Functional completeness of definite subspaces in Krein space.
G. Stolz: Expansion in generalized eigenfunctions of Schrödinger operators with singular potentials.
S. Sun: Duality and Hankel operators.
H. Widom: Eigenvalue distribution of non-selfadjoint Toeplitz matrices and the asymptotics of Toeplitz determinants in the case of nonvanishing index.
D. Xia: On some classes of hyponormal tuples of commuting operators.
Most of these articles presents deep new results. Probably only a few specialists will buy this book for their personal library, but every mathematical library should have this volume.