Download or read book Biorthogonal Systems in Banach Spaces written by Petr Hajek and published by Springer Science & Business Media. This book was released on 2007-10-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.
Download or read book Biorthogonal Systems of Functions written by Anna Johnson Pell and published by . This book was released on 1911 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bases and Biorthogonal Systems in C O 1 written by James Robert Holub and published by . This book was released on 1966 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2013 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2003 with total page 1808 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings written by Library of Congress. Office for Subject Cataloging Policy and published by . This book was released on 1992 with total page 1352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Orthogonal Polynomials in Two Variables written by P.K. Suetin and published by Routledge. This book was released on 2022-04-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.
Download or read book Non Self Adjoint Boundary Eigenvalue Problems written by R. Mennicken and published by Elsevier. This book was released on 2003-06-26 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations. In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalent to a first order system, the main techniques are developed for systems. Asymptotic fundamental systems are derived for a large class of systems of differential equations. Together with boundary conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10. The contour integral method and estimates of the resolvent are used to prove expansion theorems. For Stone regular problems, not all functions are expandable, and again relatively easy verifiable conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable. Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated. Key features: • Expansion Theorems for Ordinary Differential Equations • Discusses Applications to Problems from Physics and Engineering • Thorough Investigation of Asymptotic Fundamental Matrices and Systems • Provides a Comprehensive Treatment • Uses the Contour Integral Method • Represents the Problems as Bounded Operators • Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions
Download or read book A Basis Theory Primer written by Christopher Heil and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.
Download or read book Introduction to the Theory of Bases written by Jürg T. Marti and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of Banach's treatise on the theory of linear operators, the literature on the theory of bases in topological vector spaces has grown enormously. Much of this literature has for its origin a question raised in Banach's book, the question whether every sepa rable Banach space possesses a basis or not. The notion of a basis employed here is a generalization of that of a Hamel basis for a finite dimensional vector space. For a vector space X of infinite dimension, the concept of a basis is closely related to the convergence of the series which uniquely correspond to each point of X. Thus there are different types of bases for X, according to the topology imposed on X and the chosen type of convergence for the series. Although almost four decades have elapsed since Banach's query, the conjectured existence of a basis for every separable Banach space is not yet proved. On the other hand, no counter examples have been found to show the existence of a special Banach space having no basis. However, as a result of the apparent overconfidence of a group of mathematicians, who it is assumed tried to solve the problem, we have many elegant works which show the tight connection between the theory of bases and structure of linear spaces.
Download or read book Functional Analysis and Operator Theory written by Volodymyr Brayman and published by Springer Nature. This book was released on with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Frames and Riesz Bases written by Ole Christensen and published by Springer Science & Business Media. This book was released on 2002-12-13 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Applied and Numerical Harmonic Analysis ( ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har monic analysis to basic applications. The title of the series reflects the im portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.
Download or read book Wavelet Analysis written by Howard L. Resnikoff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text gives a clear introduction to the ideas and methods of wavelet analysis, making concepts understandable by relating them to methods in mathematics and engineering. It shows how to apply wavelet analysis to digital signal processing and presents a wide variety of applications.
Download or read book Frames and Bases written by Ole Christensen and published by Springer Science & Business Media. This book was released on 2008-06-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a streamlined presentation of the author’s successful work, An Introduction to Frames and Riesz Bases, this book develops frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. The book presents basic results in an accessible way and includes extensive exercises.
Download or read book NASA Technical Note written by and published by . This book was released on 1965 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Denseness Bases and Frames in Banach Spaces and Applications written by Aref Jeribi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory
Download or read book Multivariate Approximation Theory II written by Schempp and published by Birkhäuser. This book was released on 2012-12-06 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Third International Symposium on Hultivariate Approximation Theory was held at the Oberwolfach!1athematical Research Insti tute, Black Forest, February 8-12, 1982. The preceding conferen ces on this topic were held in 1976* and 1979**. The conference brought together 50 mathematicians from 14 coun tries. These Proceedings form arecord of most of the papers pre sented at the Symposium. The topics treated cover different problems on multivariate approximation theory such as new results concerning approxima tion by polynomials in Sobolev spaces, biorthogonal systems and orthogonal series of functions in several variables, multivariate spline functions, group theoretic and functional analytic methods, positive linear operators, error estimates for approximation procedures and cubature formulae, Boolean methods in multivari ate interpolation and the numerical application of summation procedures. Special emphasis was posed on the application of multivariate approximation in various fields of science. One mathematician was sorely missed at the Symposium. Professor Arthur Sard who had actively taken part in the earlier conferen ces passed away in August of 1980. Since he was a friend of many of the participants, the editors wish to dedicate these Procee dings to the memory of this distinguished mathematician. Abrief appreciation of his life and mathematical work appears as well *"Constructive Theory of Functions of Several Variables". Edited by w. Schempp and Karl Zeller. Lecture Notes in 1-1athematics, Vol
