Reproducing Kernel Spaces and Applications

ISBN-13: 9783034894302 / Angielski / Miękka / 2012 / 344 str.

Daniel Alpay

Opis

The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition.
The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems, several complex variables, and the non-commutative case.
The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Spis treści

Realization of Functions into the Symmetrised Bidisc.- A Basic Interpolation Problem for Generalized Schur Functions and Coisometric Realizations.- Formal Reproducing Kernel Hilbert Spaces: The Commutative and Noncommutative Settings.- On Realizations of Rational Matrix Functions of Several Complex Variables II.- Bergman Projection and Weighted Holomorphic Functions.- Linear Fractional Transformations, Riccati Equations and Bitangential Interpolation, Revisited.- A Class of Matrix-valued Schrödinger Operators with Prescribed Finite-band Spectra.- Laplace Transforms Asymptotics, Bergman Kernels and Composition Operators.- On the Structure of Self-similar Systems: A Hilbert Space Approach.- Reproducing Kernels and a Family of Bounded Linear Operators.- Multipliers in the Reproducing Kernel Hilbert Space, Subnormality and Noncommutative Complex Analysis.- Existence of Unitary Dilations as a Moment Problem.