Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers.

Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role.

The contributions in this volume reflect Heinz Langer's chief research interests and will appeal to a broad readership whose work involves operator theory.

Contenu
Part I - Biographical material.- List of publications of Heinz Langer.- Program of the Laudatio ceremony and photos.- Heinz Langer Laudatio.- Part II - Papers.- The inverse monodromy problem.- The bitangential matrix Nevanlinna-Pick interpolation problem revisited.- Finite rank perturbations in Pontryagin spaces and a Sturm-Liouville problem with -rational boundary conditions.- On unimodular transformations of conservative L-systems.- Spectral theory of stationary random fi elds and their generalizations. A short historical survey.- Semicircular-like, and semicircular laws induced by certain C*-probability spaces over the fi nite adele ring AQ.- On the asymptotic behaviour of the zeros of solutions of one functional-differential equation with rescaling.- Rational q x q Carathéodory functions and central non-negative Hermitian measures.- On the spectrum of an operator in truncated Fock space.- Limit properties of eigenvalues in spectral gaps.- Self-adjoint boundary conditions for the prolate spheroid differential operators.- An addendum to a paper by Li and Zhang.- On accelerants and their analogs, and on the characterization of the rectangular Weyl functions for Dirac systems with locally square-integrable potentials on a semi-axis.- Dirac equation: the stationary and dynamical scattering problems.- Compressed resolvents, Q-functions and h0-resolvents in almost Pontryagin spaces.- Dissymmetrising inner product spaces.