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Wednesday, July 22, 2020 | History

5 edition of The Schur Algorithm, Reproducing Kernel Spaces and System Theory found in the catalog.

The Schur Algorithm, Reproducing Kernel Spaces and System Theory

by Daniel Alpay

  • 122 Want to read
  • 34 Currently reading

Published by American Mathematical Society .
Written in English

    Subjects:
  • Functional analysis,
  • Mathematical theory of computation,
  • Systems analysis & design,
  • Mathematics,
  • Science/Mathematics,
  • Transformations,
  • Group Theory,
  • Set Theory,
  • Study & Teaching,
  • Hilbert space,
  • Kernel functions,
  • Schur functions,
  • System theory

  • Edition Notes

    ContributionsStephen S. Wilson (Translator)
    The Physical Object
    FormatMass Market Paperback
    Number of Pages150
    ID Numbers
    Open LibraryOL11419923M
    ISBN 100821821555
    ISBN 109780821821558

    2 Reproducing Kernel Hilbert Spaces A Reproducing Kernel Hilbert Space (RKHS) is a Hilbert space Hwith a reproducing kernel whose span is dense in H. We could equivalently define an RKHS as a Hilbert space of functions with all evaluation functionals bounded and linear. For instance, the L 2 space is a Hilbert space, but not an RKHS because. There exists a Hilbert space for which a CI kernel is a reproducing kernel. Actually, property 3 can be obtained explicitly by verifying that the inequality of equation is implied by equations A.1 and A.2 in the proof of property 2 (see the appendix).

    Product Information. 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. lated in terms of the Theory of System Realizations (See [KaVo1] and [KaVo2]. For our purposes, the theory developed in [Ka] is most relevant). The current state of System Theory, as a branch of pure mathematics, is presented in [Nik]. In the present paper we show how the Schur algorithm .

    Using reproducing kernel Hilbert spaces methods we develop a Schur-type algorithm for a subclass of the functions analytic and contractive in the ball. We also consider the Nevanlinna–Pick interpolation problem in that class. The Schur algorithm, reproducing kernel spaces and system theory () 4 Patrick le Calvez Dynamical properties of diffeomorphisms of the annulus and of the torus () 3 Bernadette Perrin-Riou p-adic functions and p-adic representations () 2 Michel Zinsmeister Thermodynamic formalism and holomorphic dynamical systems () 1 Claire Voisin.


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The Schur Algorithm, Reproducing Kernel Spaces and System Theory by Daniel Alpay Download PDF EPUB FB2

In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory 5/5(1).

This book is an impressive survey of recent research in the applications of Reproducing Kernel Hilbert Spaces to complex analytic function theory, and, in particular to the study of functions which are analytic on the open unit disk in the complex plane.5/5.

The same positive functions (in the sense of reproducing kernel spaces) appear in a natural way in two different domains, namely the modeling of time-invariant dissipative linear systems and the theory of linear operators. We use the associated reproducing kernel Hilbert spaces to study the relationships between these domains.

The inverse scattering problem plays a key role in the by: ISBN: OCLC Number: Description: viii, pages: illustrations ; 26 cm.

Contents: Reproducing kernel spaces --Definition and first examples --Interpolation and reproducing kernels --Initial properties --Operators in a reproducing kernel space --Complementation and matrix theory --Spaces associated with transfer functions --Leech's theorem and applications.

Request PDF | The Schur Algorithm, Reproducing Kernel Spaces and System Theory | The same positive functions (in the sense of reproducing kernel spaces) appear in a natural way in two different Author: Daniel Alpay.

The Schur Algorithm, Reproducing Kernel Spaces and System Theory by Daniel Alpay The Schur Algorithm, Reproducing Kernel Spaces and System Theory by Daniel Alpay PDF, ePub eBook D0wnl0ad The class of Schur functions consists of analytic functions on.

and [13] for applications to number theory) and the case of upper triangular operators (see [16]). It was studied using reproducing kernel Hilbert spaces methods in [4]. In the present paper we study the Schur algorithm for Schur multipliers of the ball (the definition is given in Section 2) using the reproducing kernel approach.

We follow. Idiots Tree Felling Fails with Chainsaw Machine - Tree Falls on Head and House - Duration: Woodart Presents Recommended for you. Using reproducing kernel Hilbert spaces methods we develop a Schur-type algorithm for a subclass of the functions analytic and contractive in the ball.

We also consider the Nevanlinna–Pick interpolation problem in that class. Alpay, The Schur Algorithm, Reproducing Kernel Spaces and System Theory (Translation of book: Algorithme de Schur, espaces noyau reproduisant et théorie des systémes. Panoramas et Synthéses, vol. 6 (Société Mathématique de France, )).

Schur Methods in Operator Theory and Signal Processing. Editors (view affiliations) I. Gohberg; Book. Citations; Downloads; Part of the Operator Theory: Advances and Applications book series (OT, volume 18) Log in to check access On Applications of Reproducing Kernel Spaces to the Schur Algorithm and Rational J Unitary Factorization.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Quite often a given question is best understood in a reproducing kernel Hilbert space (for instance when using Cauchy's formula in the Hardy space H) 2 and one finds oneself as Mr Jourdain of Moliere' Bourgeois Gentilhomme speaking Prose without knowing it [48, p.

51]: Par ma foil il y a plus de quarante ans que je dis de la prose sans que l j. System Theory, the Schur Algorithm and Multidimensional Analysis Alpay D., Vinnikov V. (Ed) This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion.

Reproducing Kernel Spaces and Applications inbunden,Engelska, ISBN 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.

Definition. Let be an arbitrary set and a Hilbert space of real-valued functions evaluation functional over the Hilbert space of functions is a linear functional that evaluates each function at a point: ↦ ∀ ∈. We say that H is a reproducing kernel Hilbert space if, for all in, is continuous at any in or, equivalently, if is a bounded operator on, i.e.

there exists some M > 0. Uses a variety of non-trivial and interesting examples as exercises (for instance the Bohr phenomenon, integral representations of certain analytic functions, Blaschke products, and the Schur algorithm) Exercises include those using positive definite functions and reproducing kernel spaces.

The first approach involves the tangential Schur algorithm, which employs linear fractional transformations. It stems from the theory of reproducing kernel Hilbert spaces and enables the direct construction of overlapping local parametrizations using Schur parameters and interpolation points.

The Schur Algorithm, Reproducing Kernel Spaces and System Theory. Article. an essentially new notion in linear system theory, then provides a powerful tool for computing this factorization.

The Schur Algorithm, Reproducing Kernel Spaces and System Theory. American Mathematical Society, Google Scholar; Nachman Aronszajn. Theory of reproducing kernels.

Transactions of the American Mathematical Society, 69(3), Google Scholar Cross Ref; Francis R. Bach and Michael I. Jordan. Kernel independent component analysis.

Uses a variety of non-trivial and interesting examples as the basis for exercises (e.g. the Bohr phenomenon, integral representations of certain analytic functions, Blaschke products, and the Schur algorithm) Some of the exercises use the notions of positive matrix, positive definite function and reproducing kernel Hilbert space; see more benefits.'The purpose of this fine monograph is two-fold.

On the one hand, the authors introduce a wide audience to the basic theory of reproducing kernel Hilbert spaces (RKHS), on the other hand they present applications of this theory in a variety of areas of mathematics the authors have succeeded in arranging a very readable modern presentation of RKHS and in conveying the relevance of this.This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars.

It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear.