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 Bessmertnyi 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
Summary
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 pr
