Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations - Alpay, Daniel; Vinnikov, Victor; SpringerLink (Online service) (Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2005)
Operator theory, system theory, scattering theory, and the theory of analytic functions of one complex variable are deeply related topics, and the relationships between these theories are well understood. When one leaves the setting of one operator and considers several operators, the situation is much more involved. There is no longer a single underlying theory, but rather different theories, some of them loosely connected and some not connected at all. These various theories, which one could call "multidimensional operator theory", are topics of active and intensive research. The present volume contains a selection of papers in multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. The volume will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Functional Models for Representations of the Cuntz Algebra -- Relations on Non-commutative Variables and Associated Orthogonal Polynomials -- Functions of Several Variables in the Theory of Finite Linear Structures Part I: Analysis -- Operator Method for Solution of PDEs Based on Their Symmetries -- On the Bessmertny? Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes -- Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functions II -- Preservation of the Norms of Linear Operators Acting on Some Quaternionic Function Spaces -- Hardy Algebras Associated with W*-Correspondences (Point Evaluation and Schur Class Functions) -- Notes on Generalized Lemniscates -- One-Sided Tangential Interpolation for Hilbert-Schmidt Operator Functions with Symmetries on the Bidisk -- Favard’s Theorem Modulo an Ideal.
Keywords: Mathematical analysis; Analysis (Mathematics).; Operator theory; Functions of complex variables; Differential equations; Analysis; Operator Theory; Functions of a Complex Variable; Ordinary Differential Equations