Constructive Aspects Of Functional Analysis
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| Author | : Giuseppe Geymonat |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 848 |
| Release | : 2011-06-21 |
| Genre | : Mathematics |
| ISBN | : 3642109845 |
A. Balakrishnan: A constructive approach to optimal control.- R. Glowinski: Méthodes itératives duales pour la minimisation de fonctionnelles convexes.- J.L. Lions: Approximation numérique des inéquations d’évolution.- G. Marchuk: Introduction to the methods of numerical analysis.- U. Mosco: An introduction to the approximate solution of variational inequalities.- I. Singer: Best approximation in normed linear spaces.- G. Strang: A Fourier analysis of the finite element variational method.- M. Zerner: Caractéristiques d’approximation des compacts dans les espaces fonctionnels et problèmes aux limites elliptiques.
| Author | : Centro internazionale matematico estivo |
| Publisher | : |
| Total Pages | : 516 |
| Release | : 1973 |
| Genre | : Functional analysis |
| ISBN | : |
| Author | : Douglas S. Bridges |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 227 |
| Release | : 2007-04-30 |
| Genre | : Mathematics |
| ISBN | : 0387381473 |
This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces and with associated results about operators and their adjoints on a Hilbert space. The first appendix gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. No background in intuitionistic logic or constructive analysis is needed in order to read the book, but some familiarity with the classical theories of metric, normed and Hilbert spaces is necessary.
| Author | : E. Bishop |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 490 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642616674 |
This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author. Truly, FCA was an exceptional book, not only because of the quantity of original material it contained, but also as a demonstration of the practicability of a program which most ma thematicians believed impossible to carry out. Errett's book went out of print shortly after its publication, and no second edition was produced by its publishers. Some years later, 'by a set of curious chances', it was agreed that a new edition of FCA would be published by Springer Verlag, the revision being carried out by me under Errett's supervision; at the same time, Errett gener ously insisted that I become a joint author. The revision turned out to be much more substantial than we had anticipated, and took longer than we would have wished. Indeed, tragically, Errett died before the work was completed. The present book is the result of our efforts. Although substantially based on FCA, it contains so much new material, and such full revision and expansion of the old, that it is essentially a new book. For this reason, and also to preserve the integrity of the original, I decided to give our joint work a title of its own. Most of the new material outside Chapter 5 originated with Errett.
| Author | : G. Geymonat |
| Publisher | : |
| Total Pages | : |
| Release | : 1972 |
| Genre | : Mathematics |
| ISBN | : 9788870833478 |
| Author | : Allen A. Goldstein |
| Publisher | : Courier Corporation |
| Total Pages | : 194 |
| Release | : 2012-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486488799 |
This text introduces students of mathematics, science, and technology to the methods of applied functional analysis and applied convexity. The three-part treatment consists of roots and extremal problems, constraints, and infinite dimensional problems. Topics include iterations and fixed points, metric spaces, nonlinear programming, polyhedral convex programming, linear spaces and convex sets, and applications to integral equations. 1967 edition.
| Author | : Steven G. Krantz |
| Publisher | : MAA |
| Total Pages | : 151 |
| Release | : 2013-06-06 |
| Genre | : Mathematics |
| ISBN | : 0883853574 |
This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.
| Author | : Erwin Kreyszig |
| Publisher | : John Wiley & Sons |
| Total Pages | : 706 |
| Release | : 1991-01-16 |
| Genre | : Mathematics |
| ISBN | : 0471504599 |
KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry
| Author | : Vilmos Komornik |
| Publisher | : Springer |
| Total Pages | : 417 |
| Release | : 2016-06-03 |
| Genre | : Mathematics |
| ISBN | : 1447168119 |
This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.
| Author | : Mark Bridger |
| Publisher | : John Wiley & Sons |
| Total Pages | : 323 |
| Release | : 2011-10-14 |
| Genre | : Mathematics |
| ISBN | : 1118031563 |
A unique approach to analysis that lets you apply mathematics across a range of subjects This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. In particular, existence is never established by showing that the assumption of non-existence leads to a contradiction. The ultimate consequence of this method is that it makes sense—not just to math majors but also to students from all branches of the sciences. The text begins with a construction of the real numbers beginning with the rationals, using interval arithmetic. This introduces readers to the reasoning and proof-writing skills necessary for doing and communicating mathematics, and it sets the foundation for the rest of the text, which includes: Early use of the Completeness Theorem to prove a helpful Inverse Function Theorem Sequences, limits and series, and the careful derivation of formulas and estimates for important functions Emphasis on uniform continuity and its consequences, such as boundedness and the extension of uniformly continuous functions from dense subsets Construction of the Riemann integral for functions uniformly continuous on an interval, and its extension to improper integrals Differentiation, emphasizing the derivative as a function rather than a pointwise limit Properties of sequences and series of continuous and differentiable functions Fourier series and an introduction to more advanced ideas in functional analysis Examples throughout the text demonstrate the application of new concepts. Readers can test their own skills with problems and projects ranging in difficulty from basic to challenging. This book is designed mainly for an undergraduate course, and the author understands that many readers will not go on to more advanced pure mathematics. He therefore emphasizes an approach to mathematical analysis that can be applied across a range of subjects in engineering and the sciences.
