Download or read book Collectively Compact Operator Approximation Theory and Applications to Integral Equations written by Philip M. Anselone and published by Prentice Hall. This book was released on 1971 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Collectively Compact Operator Approximation Theory and Applications to Integral Equations written by Philip M. Anselone and published by . This book was released on 1971 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Collectively compact operator approximations theory and applications to integral equations written by Philip M. Anselone and published by . This book was released on 1971 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Collectively Compact Operator Theory to the Existence of Eigenvalues of Integral Equations written by Christina Josephine Mirkovich and published by . This book was released on 1974 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of eigenvalues is shown for certain types of integral equations with continuous kernels, the proofs utilizing some basic results of collectively compact operator approximation theory.
Download or read book On the Uniform Approximation of a Class of Singular Integral Equations in a H lder Space written by Allan William McInnes and published by . This book was released on 1972 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Operators Collective Compactness and the Spectral Theory of Infinite Matrices written by Simon N. Chandler-Wilde and published by American Mathematical Soc.. This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first half of this memoir the authors explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). They build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator $A$ (its operator spectrum). In the second half of this memoir the authors study bounded linear operators on the generalised sequence space $\ell^p(\mathbb{Z}^N,U)$, where $p\in [1,\infty]$ and $U$ is some complex Banach space. They make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator $A$ is a locally compact perturbation of the identity. Especially, they obtain stronger results than previously known for the subtle limiting cases of $p=1$ and $\infty$.
Download or read book Collectively Compact Operator Approximations Lectures Presented July august 1967 written by P. M. Anselone and published by . This book was released on 1967 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general approximation theory for linear and nonlinear operators on Banach spaces is presented. It is applied to numerical integration approximations of integral operators. Convergence of the operator approximations is pointwise rather than uniform on bounded sets, which is assumed in other theories. The operator perturbations form a collectively compact set, i.e., they map each bounded set into a single compact set. In the nonlinear case, Frechet differentiability conditions are also imposed. Principal results include convergence and error bounds for approximate solutions and, for linear operators, results on spectral approximations. (Author).
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1988 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.
Download or read book Integral Equations written by Wolfgang Hackbusch and published by Birkhäuser. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
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 Linear Operator Equations written by M. Thamban Nair and published by World Scientific. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Download or read book The Theory of Approximate Methods and Their Applications to the Numerical Solution of Singular Integral Equations written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 1976-06-30 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Operator Equations Approximation And Regularization written by M Thamban Nair and published by World Scientific. This book was released on 2009-05-05 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Download or read book Proceedings of the Conference on Differential Difference Equations and Applications written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 1266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Numerical Solution of Integral Equations of the Second Kind written by Kendall E. Atkinson and published by Cambridge University Press. This book was released on 1997-06-28 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive introduction to the numerical solution of a large class of integral equations.
Download or read book Weighted Polynomial Approximation and Numerical Methods for Integral Equations written by Peter Junghanns and published by Springer Nature. This book was released on 2021-08-10 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.
Download or read book Approximation Theory Sequence Spaces and Applications written by S. A. Mohiuddine and published by Springer Nature. This book was released on 2022-12-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.
