From Complex Analysis to Operator Theory: A Panorama

ISBN-13: 9783031311383 / Angielski / Twarda / 2023

Opis

This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Spis treści

Part I On Some of Sergey’s Works.- Working with Sergey Naboko on Boundary Triples.- Operator-Valued Nevanlinna–Herglotz Functions, Trace Ideals, and Sergey Naboko’s Contributions.- Mathematical Heritage of Sergey Naboko: Functional Models of Non-Self-Adjoint Operators.- On Crossroads of Spectral Theory with Sergey Naboko.- Sergey Naboko’s Legacy on the Spectral Theory of Jacobi Operators.- On theWork by Serguei Naboko on the Similarity to Unitary and Selfadjoint Operators.- Part II Research Contributions.- Functional Models of Symmetric and Selfadjoint Operators.- Schrödinger Operators with δ-potentials Supported on Unbounded Lipschitz Hypersurfaces.- Improved Lieb–Thirring Type Inequalities for Non-selfadjoint Schrödinger Operators.- Ballistic Transport in Periodic and Random Media.- On the Spectral Theory of Systems of First Order Equations with Periodic Distributional Coefficients.- Asymptotic Analysis of Operator Families and Applications to Resonant Media.- On the Number and Sums of Eigenvalues of Schrödinger-type Operators with Degenerate Kinetic Energy.- Gap Labelling for Discrete One-Dimensional Ergodic Schrödinger Operators.- Degenerate Elliptic Operators and Kato’s Inequality.- Generalized Indefinite Strings with Purely Discrete Spectrum.- Soliton Asymptotics for the KdV Shock Problem of Low Regularity.- Realizations of Meromorphic Functions of Bounded Type.- Spectral Transition Model with the General Contact Interaction.- Weyl’s Law under Minimal Assumptions.- Weyl–Titchmarsh M-Functions for ϕ-Periodic Sturm–Liouville Operators in Terms of Green’s Functions.- On Discrete Spectra of Bergman–Toeplitz Operators with Harmonic Symbols.- One Dimensional Discrete Schrödinger Operators with Resonant Embedded Eigenvalues.- On the Invariance Principle for a Characteristic Function.- A Trace Formula and Classical Solutions to the KdV Equation.- Semiclassical Analysis in the Limit Circle Case.