Operator Theory

Indefinite Hamiltonian Systems.- Locally Definitizable Operators: The Local Structure of Spectrum.- Multi-valued Operators/Linear Relations Between Krein Spaces.- Reproducing Kernel Krein Spaces.- Schur Analysis in an Indefinite Setting.- Symmetric and Isometric Relations.- The Algebraic Ricatti Equation and Its Role in Indefinite Inner Product Spaces.- The Critical Point Infinity Associated with Indefinite Sturm-Liouville Problems.- A Von Neumann Algebra over the Adele Ring and the Euler Totient Function.- Arithmetic Functions in Harmonic Analysis and Operator Theory.- Unbounded Operators, Lie Algebras, and Local Representations.- Linear Transforms in Signal and Optical Systems.- Realization of Herglotz-Nevanlinna Functions by Conservative Systems.- Robust Stabilization of Linear Control Systems Using A Frequency Domain Approach.- Semi-Separable Systems: Representations, Inversion, and Limiting Behavior.- Synchronization Problems for Spatially Invariant Infinite Dimensional Linear Systems.- Commutative Dilation Theory.- Operator Theory and Function Theory in Drury-Arveson Space and Its Quotients.- Taylor Functional Calculus.- Sampling Theory and Reproducing Kernel Hilbert Spaces.- Quaternionic Analysis: Application to Boundary Value Problems.- An Introduction to Hilbert Module Approach to Multivariable Operator Theory.- Applications of Hilbert Module Approach to Multivariable Operator Theory.- Perturbations of Unbounded Fredholm Linear Operators in Banach Spaces.

Prof. Daniel Alpay is a faculty member of the department of mathematics at Ben-Gurion University, Beer-Sheva, Israel. He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University. Together with co-authors, he has written two books and close to 190 research papers, and edited ten books of research papers.