Fundamentals Of Functional Analysis PDF Download
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Author | : Douglas Farenick |
Publisher | : Springer |
Total Pages | : 455 |
Release | : 2016-10-24 |
Genre | : Mathematics |
ISBN | : 3319456334 |
Download Fundamentals of Functional Analysis Book in PDF, ePub and Kindle
This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.
Author | : Semën Samsonovich Kutateladze |
Publisher | : Springer Science & Business Media |
Total Pages | : 289 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401587558 |
Download Fundamentals of Functional Analysis Book in PDF, ePub and Kindle
to the English Translation This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces. With standard provisos the presentation is self-contained, exposing about a h- dred famous "named" theorems furnished with complete proofs and culminating in the Gelfand-Nalmark-Segal construction for C*-algebras. The first Russian edition was printed by the Siberian Division of "Nauka" P- lishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk. This volume is translated from the second Russian edition printed by the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences· in 1995. It incorporates new sections on Radon measures, the Schwartz spaces of distributions, and a supplementary list of theoretical exercises and problems. This edition was typeset using AMS-'lEX, the American Mathematical Society's 'lEX system. To clear my conscience completely, I also confess that := stands for the definor, the assignment operator, signifies the end of the proof.
Author | : Martin Schechter |
Publisher | : American Mathematical Soc. |
Total Pages | : 450 |
Release | : 2001-11-13 |
Genre | : Mathematics |
ISBN | : 0821828959 |
Download Principles of Functional Analysis Book in PDF, ePub and Kindle
This excellent book provides an elegant introduction to functional analysis ... carefully selected problems ... This is a nicely written book of great value for stimulating active work by students. It can be strongly recommended as an undergraduate or graduate text, or as a comprehensive book for self-study. --European Mathematical Society Newsletter Functional analysis plays a crucial role in the applied sciences as well as in mathematics. It is a beautiful subject that can be motivated and studied for its own sake. In keeping with this basic philosophy, the author has made this introductory text accessible to a wide spectrum of students, including beginning-level graduates and advanced undergraduates. The exposition is inviting, following threads of ideas, describing each as fully as possible, before moving on to a new topic. Supporting material is introduced as appropriate, and only to the degree needed. Some topics are treated more than once, according to the different contexts in which they arise. The prerequisites are minimal, requiring little more than advanced calculus and no measure theory. The text focuses on normed vector spaces and their important examples, Banach spaces and Hilbert spaces. The author also includes topics not usually found in texts on the subject. This Second Edition incorporates many new developments while not overshadowing the book's original flavor. Areas in the book that demonstrate its unique character have been strengthened. In particular, new material concerning Fredholm and semi-Fredholm operators is introduced, requiring minimal effort as the necessary machinery was already in place. Several new topics are presented, but relate to only those concepts and methods emanating from other parts of the book. These topics include perturbation classes, measures of noncompactness, strictly singular operators, and operator constants. Overall, the presentation has been refined, clarified, and simplified, and many new problems have been added. The book is recommended to advanced undergraduates, graduate students, and pure and applied research mathematicians interested in functional analysis and operator theory.
Author | : Michel Willem |
Publisher | : Springer Nature |
Total Pages | : 259 |
Release | : 2023-01-27 |
Genre | : Mathematics |
ISBN | : 3031091493 |
Download Functional Analysis Book in PDF, ePub and Kindle
This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis in relation to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students in mathematics and applied mathematics. The second edition of Functional Analysis includes several improvements as well as the addition of supplementary material. Specifically, the coverage of advanced calculus and distribution theory has been completely rewritten and expanded. New proofs, theorems, and applications have been added as well for readers to explore.
Author | : Christian Clason |
Publisher | : Springer Nature |
Total Pages | : 166 |
Release | : 2020-11-30 |
Genre | : Mathematics |
ISBN | : 3030527840 |
Download Introduction to Functional Analysis Book in PDF, ePub and Kindle
Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.
Author | : Markus Haase |
Publisher | : American Mathematical Society |
Total Pages | : 394 |
Release | : 2014-09-17 |
Genre | : Mathematics |
ISBN | : 0821891715 |
Download Functional Analysis Book in PDF, ePub and Kindle
This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn-Banach theorem provide a stepping-stone to more advanced texts. The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level.
Author | : Erwin Kreyszig |
Publisher | : John Wiley & Sons |
Total Pages | : 706 |
Release | : 1991-01-16 |
Genre | : Mathematics |
ISBN | : 0471504599 |
Download Introductory Functional Analysis with Applications Book in PDF, ePub and Kindle
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 | : Sterling K. Berberian |
Publisher | : Springer Science & Business Media |
Total Pages | : 504 |
Release | : 2013-03-15 |
Genre | : Mathematics |
ISBN | : 9780387984803 |
Download Fundamentals of Real Analysis Book in PDF, ePub and Kindle
"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS
Author | : Fabio Botelho |
Publisher | : Springer |
Total Pages | : 584 |
Release | : 2014-06-12 |
Genre | : Mathematics |
ISBN | : 3319060740 |
Download Functional Analysis and Applied Optimization in Banach Spaces Book in PDF, ePub and Kindle
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Author | : Dragisa Mitrovic |
Publisher | : CRC Press |
Total Pages | : 416 |
Release | : 1997-11-12 |
Genre | : Mathematics |
ISBN | : 9780582246942 |
Download Fundamentals of Applied Functional Analysis Book in PDF, ePub and Kindle
This volume provides an introduction to modern concepts of linear and nonlinear functional analysis. Its purpose is also to provide an insight into the variety of deeply interlaced mathematical tools applied in the study of nonlinear problems.