Download or read book Interpolation of Rational Matrix Functions written by Joseph Ball and published by Birkhäuser. This book was released on 2013-11-11 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).

Download or read book Topics in Interpolation Theory of Rational Matrix valued Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2013-11-21 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.

Download or read book Topics in Interpolation Theory of Rational Matrix valued Functions written by Israel Gohberg and published by . This book was released on 1988 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Interpolation by Rational Matrix Functions with Minimal McMillan Degree written by Jeongook Kim Kang and published by . This book was released on 1990 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Zero pole Interpolation of Nonregular Rational Matrix Functions written by Marek Rakowski and published by . This book was released on 1989 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Extension and Interpolation of Linear Operators and Matrix Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2013-11-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Some Interpolation Problems for Rational Matrix valued Functions written by Richard Ernest Faulkenberry and published by . This book was released on 1990 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book J Contractive Matrix Functions Reproducing Kernel Hilbert Spaces and Interpolation written by Harry Dym and published by American Mathematical Soc.. This book was released on 1989 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the theory and applications of $J$ inner matrices. This book discusses matrix interpolation problems including two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these.

Download or read book On Some Interpolation Problems for Rational Matrix valued Functions written by and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Zero pole Interpolation of Nonregular Rational Matrix Functions written by Marek Rakowski (elektronika) and published by . This book was released on 1990 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Interpolation and Approximation by Rational Functions in the Complex Domain written by J. L. Walsh and published by American Mathematical Soc.. This book was released on 1935-12-31 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

Download or read book Topics in Interpolation Theory of Rational Matrix valued Functions written by I. Gohberg and published by Birkhäuser. This book was released on 1988-01-01 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.

Download or read book Interpolation Schur Functions and Moment Problems II written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.​

Download or read book New Aspects in Interpolation and Completion Theories written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of eight papers containing recent advances in interpolation theory for matrix functions and completion theory for matrices and operators. In the first paper, D. Alpay and P. Loubaton, "The tangential trigonometric moment problem on an interval and related topics" a trigonometric moment problem on an interval for matrix valued functions is studied. The realization approach plays an important role in solving this problem. The second paper, M. Bakonyi, V.G. Kaftal, G. Weiss and H.J. Woerdeman, "Max imum entropy and joint norm bounds for operator extensions" is dedicated to a matrix completion problem. In it is considered the problem when only the lower triangular part of the operator entries of a matrix is identified. Completions which have simultaneously a small usual norm and a small Hilbert-Schmidt norm are considered. Bounds for these norms are obtained. The analysis of the maximum entropy extension plays a special role. The paper contains applications to nest algebras and integral operators. The third paper, J .A. Ball, I. Gohberg and M.A. Kaashoek, "Bitangential interpola tion for input-output operators of time varying systems: the discrete time case" contains solutions of time varying interpolation problems. The main attention is focused on the time varying analog of the Nevanlinna-Pick tangential problem in the case where the inter polation conditions appear from two sides. The state space theory of time varying systems play an important role.

Download or read book Matrix Functions of Bounded Type An Interplay Between Function Theory and Operator Theory written by Raúl E. Curto and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér Interpolation Problem for matrix rational functions. The authors then extend the H∞-functional calculus to an H∞¯¯¯¯¯¯¯¯¯+H∞-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of 2×2 partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.

Download or read book Lectures on Operator Theory and Its Applications written by Albrecht Böttcher and published by American Mathematical Soc.. This book was released on 1996 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of the importance of mathematics lies in its ability to provide theories which are useful in widely different fields of endeavour. A good example is the large and amorphous body of knowledge known as the theory of linear operators or operator theory, which came to life about a century ago as a theory to encompass properties common to matrix, differential, and integral operators. Thus, it is a primary purpose of operator theory to provide a coherent body of knowledge which can explain phenomena common to the enormous variety of problems in which such linear operators play a part. The theory is a vital part of functional analysis, whose methods and techniques are one of the major advances of twentieth century mathematics and now play a pervasive role in the modeling of phenomena in probability, imaging, signal processing, systems theory, etc, as well as in the more traditional areas of theoretical physics and mechanics. This book is based on lectures presented at a meeting on operator theory and its applications held at the Fields Institute in 1994.

Download or read book Operator Theory and Complex Analysis written by T. Ando and published by Birkhäuser. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: