Operator Theory, Analysis and Mathematical Physics

This volume contains lectures delivered by the participants of the international conference "Operator Theory, Analysis and Mathematical Physics" (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland on July 6-11, 2004. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics. The main topics are functional models of non-selfadjoint operators, spectral properties of Dirac and Jacobi matrices, Dirichlet-to-Neumann techniques, Lyapunov exponents methods, and inverse spectral problems for quantum graphs.

Résumé

This volume contains lectures delivered at the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics.

Contenu
Finiteness of Eigenvalues of the Perturbed Dirac Operator.- A Mathematical Study of Quantum Revivals and Quantum Fidelity.- On Relations Between Stable and Zeno Dynamics in a Leaky Graph Decay Model.- On the Spectrum of Partially Periodic Operators.- Functional Model for Singular Perturbations of Non-self-adjoint Operators.- Trace Formulas for Jacobi Operators in Connection with Scattering Theory for Quasi-Periodic Background.- Dirichlet-to-Neumann Techniques for the Plasma-waves in a Slot-diod.- Inverse Spectral Problem for Quantum Graphs with Rationally Dependent Edges.- Functional Model of a Class of Non-selfadjoint Extensions of Symmetric Operators.- Lyapunov Exponents at Anomalies of SL(2, ?)-actions.- Uniform and Smooth Benzaid-Lutz Type Theorems and Applications to Jacobi Matrices.- An Example of Spectral Phase Transition Phenomenon in a Class of Jacobi Matrices with Periodically Modulated Weights.- On Connection Between Factorizations of Weighted Schur Functions and Invariant Subspaces.