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| Author | : Yoav Benyamini |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 503 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821808354 |
Download Geometric Nonlinear Functional Analysis Book in PDF, ePub and Kindle
A systematic study of geometric nonlinear functional analysis. The main theme is the study of uniformly continuous and Lipschitz functions between Banach spaces. This study leads to the classification of Banach spaces and of their important subsets in the uniform and Lipschitz categories.
| Author | : Yoav Benyamini |
| Publisher | : |
| Total Pages | : |
| Release | : 1927 |
| Genre | : Mathematics |
| ISBN | : 9780821808351 |
Download Geometric Nonlinear Functional Analysis Book in PDF, ePub and Kindle
| Author | : L. Nirenberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 159 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821828193 |
Download Topics in Nonlinear Functional Analysis Book in PDF, ePub and Kindle
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems. For more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
| Author | : Tadeusz Iwaniec |
| Publisher | : Clarendon Press |
| Total Pages | : 576 |
| Release | : 2001 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198509295 |
Download Geometric Function Theory and Non-linear Analysis Book in PDF, ePub and Kindle
Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.
| Author | : Antonio Ambrosetti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 203 |
| Release | : 2011-07-19 |
| Genre | : Mathematics |
| ISBN | : 0817681140 |
Download An Introduction to Nonlinear Functional Analysis and Elliptic Problems Book in PDF, ePub and Kindle
This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.
| Author | : P. S. Milojevic |
| Publisher | : CRC Press |
| Total Pages | : 284 |
| Release | : 1989-09-28 |
| Genre | : Mathematics |
| ISBN | : 9780824782559 |
Download Nonlinear Functional Analysis Book in PDF, ePub and Kindle
This book is based on the lectures presented at the Special Session on Nonlinear Functional Analysis of the American Mathematical Society Regional Meeting, held at New Jersey Institute of Technology. It explores global invertibility and finite solvability of nonlinear differential equations.
| Author | : Charles Chidume |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 337 |
| Release | : 2009-03-27 |
| Genre | : Mathematics |
| ISBN | : 1848821891 |
Download Geometric Properties of Banach Spaces and Nonlinear Iterations Book in PDF, ePub and Kindle
The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
| Author | : Nikolaos S. Papageorgiou |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 1003 |
| Release | : 2024-07-01 |
| Genre | : Mathematics |
| ISBN | : 3111288323 |
Download Applied Nonlinear Functional Analysis Book in PDF, ePub and Kindle
The second edition covers the introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. The new edition includes some new topics on Banach spaces of functions and measures and nonlinear analysis.
| Author | : R. B. Holmes |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2012-12-12 |
| Genre | : Mathematics |
| ISBN | : 9781468493719 |
Download Geometric Functional Analysis and its Applications Book in PDF, ePub and Kindle
This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces.
| Author | : Ilya J. Bakelman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 524 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642698816 |
Download Convex Analysis and Nonlinear Geometric Elliptic Equations Book in PDF, ePub and Kindle
Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
