Collectively Compact Operator Approximation Theory and Applications to Integral Equations
Author: Philip M. Anselone
Publisher: Prentice Hall
Published: 1971
Total Pages: 164
ISBN-13: 9780131406735
DOWNLOAD EBOOKRead and Download eBook Full
Author: Philip M. Anselone
Publisher: Prentice Hall
Published: 1971
Total Pages: 164
ISBN-13: 9780131406735
DOWNLOAD EBOOKAuthor: Philip M. Anselone
Publisher:
Published: 1971
Total Pages: 128
ISBN-13:
DOWNLOAD EBOOKAuthor: Christina Josephine Mirkovich
Publisher:
Published: 1974
Total Pages: 48
ISBN-13:
DOWNLOAD EBOOKThe 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.
Author: Allan William McInnes
Publisher:
Published: 1972
Total Pages: 128
ISBN-13:
DOWNLOAD EBOOKAuthor: Simon N. Chandler-Wilde
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 126
ISBN-13: 0821852434
DOWNLOAD EBOOKIn 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 $\infty$.
Author: P. M. Anselone
Publisher:
Published: 1967
Total Pages: 63
ISBN-13:
DOWNLOAD EBOOKA 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).
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
Published: 1988
Total Pages: 540
ISBN-13: 9781556080036
DOWNLOAD EBOOKV.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.
Author: Francoise Chatelin
Publisher: SIAM
Published: 2011-05-26
Total Pages: 482
ISBN-13: 0898719992
DOWNLOAD EBOOKOriginally published: New York: Academic Press, 1983.
Author: A.A. Ivanov
Publisher: Springer Science & Business Media
Published: 1976-06-30
Total Pages: 358
ISBN-13: 9789028600362
DOWNLOAD EBOOKAuthor: V. K. Dzyadyk
Publisher: VSP
Published: 1995
Total Pages: 340
ISBN-13: 9789067641944
DOWNLOAD EBOOKThis book is the result of 20 years of investigations carried out by the author and his colleagues in order to bring closer and, to a certain extent, synthesize a number of well-known results, ideas and methods from the theory of function approximation, theory of differential and integral equations and numerical analysis. The book opens with an introduction on the theory of function approximation and is followed by a new approach to the Fredholm integral equations to the second kind. Several chapters are devoted to the construction of new methods for the effective approximation of solutions of several important integral, and ordinary and partial differential equations. In addition, new general results on the theory of linear differential equations with one regular singular point, as well as applications of the various new methods are discussed.