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

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. Front Matter....Pages i-vii Heinz Langer and his work....Pages 1-22 On the spectra of some classes of quadratic operator pencils....Pages 23-36 Special realizations for Schur upper triangular operators....Pages 37-90 On the defect of noncontractive operators in Kreĭn spaces: a new formula and some applications....Pages 91-112 Positive differential operators in the Krein space L 2 (R n )....Pages 113-129 Singular values of positive pencils and applications....Pages 131-146 Perturbations of Krein spaces preserving the nonsingularity of the critical point infinity....Pages 147-155 An analysis of the block structure of j qq -inner functions....Pages 157-185 Selfadjoint extensions of the orthogonal sum of symmetric relations, II....Pages 187-200 Some interpolation problems of Nevanlinna-Pick type. The Kreĭn-Langer method....Pages 201-216 On the spectral representation for singular selfadjoint boundary eigenvalue problems....Pages 217-251 Some characteristics of a linear manifold in a Kreĭn space and their applications....Pages 253-257 Riggings and relatively form bounded perturbations of nonnegative operators in Kreĭn spaces....Pages 259-273 Norm bounds for Volterra integral operators and time-varying linear systems with finite horizon....Pages 275-290 The numerical range of selfadjoint matrix polynomials....Pages 291-304 Spectral properties of a matrix polynomial connected with a component of its numerical range....Pages 305-308 Lyapunov stability of a perturbed multiplication operator....Pages 309-326 Multiplicative perturbations of positive operators in Krein spaces....Pages 327-336 On the number of negative squares of certain functions....Pages 337-353 Factorization of elliptic pencils and the Mandelstam hypothesis....Pages 355-387 An inductive limit procedure within the quantum harmonic oscillator....Pages 389-395 Canonical systems with a semibounded spectrum....Pages 397-417 Back Matter....Pages 419-421