The subject of this book is about the ubiquity of the Schur parameters, whose introduction goes back to a paper of I. Schur in 1917 concerning an interpolation problem of C. Caratheodory. What followed there appears to be a truly fascinating story which, however, should be told by a professional historian. Here we provide the reader with a simplified version, mostly related to the contents of the book. In the twenties, thf~ theory of orthogonal polynomials on the unit circle was developed by G. Szego and the formulae relating these polynomials involved num bers (usually called Szego parameters) similar to the Schur parameters. Mean while, R. Nevanlinna and G. Pick studied the theory of another interpolation problem, known since then as the Nevanlinna-Pick problem, and an algorithm similar to Schur's one was obtained by Nevanlinna. In 1957, Z. Nehari solved OO an L problem which contained both Caratheodory-Schur and Nevannlina-Pick problems as particular cases. Apparently unrelated work of H. Weyl, J. von Neu mann and K. Friedericks concerning selfadjoint extensions of symmetric operators was connected to interpolation by M. A. Naimark and M. G Krein using some gen eral dilation theoretic ideas. Classical moment problems, like the trigonometric moment and Hamburger moment problems, were also related to these topics and a comprehensive account of what can be called the classical period has appeared in the monograph of M. G. Krein and A. A. Nudelman, [KN].

This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells

This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells.

Operator Theory: Advances and Applications. Schur Parameters, Factorization and Dilation Problems. Schur Parameters and Positive Block Matrices. Constantinescu, Tiberiu. Authors: Constantinescu, Tiberiu. eBook 53,49 €. price for Russian Federation (gross).

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Tiberiu Constantinescu. Constantinescu T. (1996) Nonstationary Processes. In: Schur Parameters, Factorization and Dilation Problems. Operator Theory Advances and Applications, vol 82. Part of the Operator Theory Advances and Applications book series (OT, volume 82). Abstract. The main purpose of this chapter is show how to use the Schur parameters in computations regarding the geometry of nonstationary processes. A typical example in this direction is the Kolmogorov-Wiener problem. The solution of this problem in terms of the Schur parameters is then compared with the classical solution of Kolmogorov and Wiener. Birkhäuser Basel.

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Start by marking Schur Parameters, Factorization, And Dilation Problems as Want to Read: Want to Read savin. ant to Read. The subject of this book is about the ubiquity of the Schur parameters, whose introduction goes back to a paper of I. Schur in 1917 concerning an interpolation problem of C. Caratheodory. What followed there appears to be a truly fascinating story which, however, should be told by a professional historian. In the twenties, thf theory of orthogonal polynomials on the unit circle was developed by G. Szego and the formulae relating these polynomials involved num bers (usually called Szego parameters) similar to the Schur parameters.

Автор: Constantinescu Tiberiu Название: Schur Parameters, Factorization and Dilation Problems .

A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells.

Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their . Applications and examples § 1. An effective solution of the inverse problem.

Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications. inverse problems § 1. The continual factorization of W(z) § 2. The inverse problem for bounded operator-valued functions § 3. The direct and the inverse spectral problems Chapter IV. An effective solution of the inverse problem § 2. Examples § 3. Interpolation problems § 4. On a class of extremal problems References.

Schur Parameters, Factorization and Dilation Problems. Tiberiu Constantinescu. Abstract This paper deals with a problem of lifting of operators in Krein spaces, with minimal signature numbers of the defects. There are obtained necessary and sufficient conditions for the. 1 Schur Parameters and Positive Block Matrices. . Renorming Hilbert Spaces and Elementary Rotations. There are obtained necessary and sufficient conditions for th. More).

This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. This part contains also applications to interpolation problems, to the problem of holomorphic equivalence and diagonalization. It is based on methods and technics of complex analysis of several variables. The first part of the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. Скачать (pdf, . 2 Mb) Читать. Epub FB2 mobi txt RTF.