Download or read book Invariant Subspaces and Approximation Theory written by Michael Jay Park and published by . This book was released on 1972 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation of Invariant Subspaces written by Faruk Yilmaz (Researcher in mathematics) and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a real number [alpha] the Dirichlet-type spaces [script D sub alpha] are the family of Hilbert spaces consisting of all analytic functions f(z) = [sum over n equals zero to infinity] [f hat of n] [z to the n] defined on the open unit disc [unit disc] such that [sum over n equals 0 to infinity] [(n+1) to alpha] [ | f hat of n |2] is finite. For [alpha] 0, the spaces [script D sub alpha] are known as weighted Bergman spaces. When [alpha]= 0, then [script D]0= H2, the well known and much studied Hardy space. For [alpha] 0, the [script D sub alpha] spaces are weighted Dirichlet spaces. The characterization of the invariant subspaces of the multiplication operator [M sub z] on the [script D sub alpha] spaces depends on [alpha], and it is partially still an open problem. The invariant subspaces of [script D]2 have been characterized in 1972 by B. I. Korenblum [25]. In this dissertation we show that the invariant subspaces of [script D]2 can be approximated by finite co-dimensional invariant subspaces. For the Dirichlet space D= [script D]1, there is no complete characterization of invariant subspaces, but we consider [D subscript E] [equals] [{f[in]D : [f superscript *] = 0 q.e. [quasi-everywhere] on E}] where E [subset] T [unit circle] is a Carleson thin set. In this case, we have a partial result. In the second part of the dissertation we prove a regularity result for extremal functions in the Dirichlet space D. If [phi] is an extremal function in the Dirichlet space, then we use a result of Richter and Sundberg [35] to show that for each point on the unit circle T the square of the absolute value of [phi] converges to its boundary value in certain tangential approach regions.
Download or read book Invariant Subspaces written by Heydar Radjavi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a large amount of work on invariant subspaces, motivated by interest in the structure of non-self-adjoint of the results have been obtained in operators on Hilbert space. Some the context of certain general studies: the theory of the characteristic operator function, initiated by Livsic; the study of triangular models by Brodskii and co-workers; and the unitary dilation theory of Sz. Nagy and Foia!? Other theorems have proofs and interest independent of any particular structure theory. Since the leading workers in each of the structure theories have written excellent expositions of their work, (cf. Sz.-Nagy-Foia!? [1], Brodskii [1], and Gohberg-Krein [1], [2]), in this book we have concentrated on results independent of these theories. We hope that we have given a reasonably complete survey of such results and suggest that readers consult the above references for additional information. The table of contents indicates the material covered. We have restricted ourselves to operators on separable Hilbert space, in spite of the fact that most of the theorems are valid in all Hilbert spaces and many hold in Banach spaces as well. We felt that this restriction was sensible since it eases the exposition and since the separable-Hilbert space case of each of the theorems is generally the most interesting and potentially the most useful case.
Download or read book Modern Approaches to the Invariant Subspace Problem written by Isabelle Chalendar and published by Cambridge University Press. This book was released on 2011-08-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Download or read book Approximation Order of Shift invariant Subspaces of L 2 R written by Gerlind Plonka and published by . This book was released on 1995 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Order of Shift Invariant Subspaces of L2 R Generated by Refinable Function Vectors written by Gerlind Plonka and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation order of shift invariant subspaces of L2 R generated by refinable function vectors written by Gerlind Plonka and published by . This book was released on 1995 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Subspaces of Matrices with Applications written by Israel Gohberg and published by SIAM. This book was released on 2006-03-01 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book addresses advanced linear algebra using invariant subspaces as the central notion and main tool. It comprehensively covers geometrical, algebraic, topological, and analytic properties of invariant subspaces, laying clear mathematical foundations for linear systems theory with a thorough treatment of analytic perturbation theory for matrix functions.
Download or read book The Computation of Bounds for the Invariant Subspaces of a General Matrix Operator written by James M. Varah and published by . This book was released on 1967 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let A be a general n x n complex matrix. We consider the problem of finding the invariant subspaces of A, i.e. solving AX = XM for X nonsingular and M block-diagonal. We first consider finding the eigensystem of A (i.e. M diagonal), assuming approximations to the eigenvalues are given. We show how to find approximate eigenvectors and rigorous machine bounds for the errors in the approximate eigensystem. Then we show how to find approximations and rigorous error bounds for higher-dimensional invariant subspaces of matrices which are close, in a sense we describe, to defective matrices, and for which poor results would be obtained for the eigensystem. Burroughs B5500 Extended Algol programs using these methods are also given. (Author).
Download or read book Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics written by Victor A. Galaktionov and published by CRC Press. This book was released on 2006-11-02 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book
Download or read book Approximation and Commutator Properties of Projections Onto Shift Invariant Subspaces and Applications to Boundary Integral Equations written by Siegfried Prössdorf and published by . This book was released on 1997 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Subspaces and Allied Topics written by Bhuri Singh Yadav and published by . This book was released on 1990 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation of Stochastic Invariant Manifolds written by Mickaël D. Chekroun and published by Springer. This book was released on 2014-12-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Download or read book Spectral Approximation of Linear Operators written by Francoise Chatelin and published by SIAM. This book was released on 2011-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Academic Press, 1983.
Download or read book Cluster Robust Error Estimates for the Rayleigh Ritz Approximation written by Evgueni Ovtchinnikov and published by . This book was released on 2004 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first part of a paper that deals with error estimates for the Rayleigh-Ritz approximations to the spectrum and invariant subspaces of a bounded Hermitian operator in a Hilbert or Euclidean space. This part addresses estimates for the angles between the invariant subspaces and their approximations via the corresponding best approximation errors and residuals and, for invariant subspaces corresponding to parts of the discrete spectrum, via eigenvalue errors.
Download or read book Lectures on Invariant Subspaces written by Henry Helson and published by Academic Press. This book was released on 2013-10-22 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Invariant Subspaces grew out of a series of lectures given gave at the University of Uppsala in the spring of 1962, and again in Berkeley the following semester. Since the subject is rather loosely defined the lecture style seemed appropriate also for this written version. The book is written for a graduate student who knows a little, but not necessarily very much, about analytic functions and about Hilbert space. The book contains 11 lectures and begins with a discussion of analytic functions. This is followed by lectures covering invariant subspaces, individual theorems, invariant subspaces in Lp, invariant subspaces in the line, and analytic vector functions. Subsequent lectures cover vectorial function theory, inner functions, range functions, and factoring of operator functions.
Download or read book Approximation Orders of and Approximation Maps from Local Principal Shift Invariant Spaces written by and published by . This book was released on 1993 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation orders of shift-invariant subspaces generated by the shifts of one compactly supported function are considered. In that course, explicit approximation maps are constructed. The approach avoids quasi- interpolation and applies to stationary and non-stationary refinements. The general results are specialized to box spline spaces, to obtain new results on their approximation orders.
