Contributions to Operator Theory in Spaces with an Indefinite Metric: The Heinz Langer Anniversary Volume

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This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th birthday.The book begins with his biography and list of publications. It contains a selection of research papers, most of which are devoted to spectral analysis of operators or operator pencils with applications to ordinary and partial differential equations. Other papers deal with time-varying systems, interpolation and ...

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Overview

This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th birthday.The book begins with his biography and list of publications. It contains a selection of research papers, most of which are devoted to spectral analysis of operators or operator pencils with applications to ordinary and partial differential equations. Other papers deal with time-varying systems, interpolation and factorization problems, and topics from mathematical physics. About half of the papers contain further developments in the theory of operators in spaces with an indefinite metric and treat new applications. The book is of interest to a wide audience of pure and applied mathematicians.

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Product Details

Table of Contents

Heinz Langer and his work 1
On the spectra of some class of quadratic operator pencils 23
Special realizations for Schur upper triangular operators 37
On the defect of noncontractive operators in Krein spaces: a new formula and some applications 91
Positive differential operators in the Krein space L[superscript 2](R[superscript n]) 113
Singular values of positive pencils and applications 131
Perturbations of Krein spaces preserving the nonsingularity of the critical point infinity 147
An analysis of the block structure of j[subscript qq]-inner functions 157
Selfadjoint extensions of the orthogonal sum of symmetric relations, II 187
Some interpolation problems of Nevaulinna-Pick type. The Krein-Langer method 201
On the spectral representation for singular selfadjoint boundary eigenvalue problems 217
Some characteristics of a linear manifold in a Krein space and their applications 253
Riggings and relatively form bounded perturbations of nonnegative operators in Krein spaces 259
Norm bounds for Volterra integral operators and time varying linear systems with finite horizon 275
The numerical range of selfadjoint matrix polynomials 291
Spectral properties of a matrix polynomial connected with a component of its numerical range 305
Lyapunov stability of a multiplication operator perturbed by a Volterra operator 309
Multiplicative perturbations of positive operators in Krein spaces 327
On the number of negative squares of certain functions 337
Factorization of elliptic pencils and the Mandelstam hypothesis 355
An inductive limit procedure within the quantum harmonic oscillator 389
Canonical systems with a semibounded spectrum 397
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