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Functional Analysis and Infinite-Dimensional Geometry

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 808/5 ( reviews)

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Book Synopsis Functional Analysis and Infinite-Dimensional Geometry by : Marian Fabian

Download or read book Functional Analysis and Infinite-Dimensional Geometry written by Marian Fabian. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

Geometric Aspects of Functional Analysis

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 907/5 ( reviews)

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Book Synopsis Geometric Aspects of Functional Analysis by : Joram Lindenstrauss

Download or read book Geometric Aspects of Functional Analysis written by Joram Lindenstrauss. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This is the sixth published volume of the Israel Seminar on Geometric Aspects of Functional Analysis. The previous volumes are 1983-84 published privately by Tel Aviv University 1985-86 Springer Lecture Notes, Vol. 1267 1986-87 Springer Lecture Notes, Vol. 1317 1987-88 Springer Lecture Notes, Vol. 1376 1989-90 Springer Lecture Notes, Vol. 1469 As in the previous vC!lumes the central subject of -this volume is Banach space theory in its various aspects. In view of the spectacular development in infinite-dimensional Banach space theory in recent years (like the solution of the hyperplane problem, the unconditional basic sequence problem and the distortion problem in Hilbert space) it is quite natural that the present volume contains substantially more contributions in this direction than the previous volumes. This volume also contains many important contributions in the "traditional directions" of this seminar such as probabilistic methods in functional analysis, non-linear theory, harmonic analysis and especially the local theory of Banach spaces and its connection to classical convexity theory in IRn. The papers in this volume are original research papers and include an invited survey by Alexander Olevskii of Kolmogorov's work on Fourier analysis (which was presented at a special meeting on the occasion of the 90th birthday of A. N. Kol mogorov). We are very grateful to Mrs. M. Hercberg for her generous help in many directions, which made the publication of this volume possible. Joram Lindenstrauss, Vitali Milman 1992-1994 Operator Theory: Advances and Applications, Vol.

An Introduction to Infinite-Dimensional Differential Geometry

2022-12-22 Mathematics
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Release : 2022-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 307/5 ( reviews)

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Book Synopsis An Introduction to Infinite-Dimensional Differential Geometry by : Alexander Schmeding

Download or read book An Introduction to Infinite-Dimensional Differential Geometry written by Alexander Schmeding. This book was released on 2022-12-22. Available in PDF, EPUB and Kindle. Book excerpt: Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.

Infinite Dimensional Analysis

2007-05-02 Business & Economics
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Release : 2007-05-02
Genre : Business & Economics
Kind : eBook
Book Rating : 960/5 ( reviews)

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Book Synopsis Infinite Dimensional Analysis by : Charalambos D. Aliprantis

Download or read book Infinite Dimensional Analysis written by Charalambos D. Aliprantis. This book was released on 2007-05-02. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst.

Open Problems in the Geometry and Analysis of Banach Spaces

2016-07-26 Mathematics
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Release : 2016-07-26
Genre : Mathematics
Kind : eBook
Book Rating : 723/5 ( reviews)

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Book Synopsis Open Problems in the Geometry and Analysis of Banach Spaces by : Antonio J. Guirao

Download or read book Open Problems in the Geometry and Analysis of Banach Spaces written by Antonio J. Guirao. This book was released on 2016-07-26. Available in PDF, EPUB and Kindle. Book excerpt: This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.

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