Author : Steven G. Krantz
Publisher : MAA
Page : 151 pages
File Size : 33,11 MB
Release : 2013-06-06
Category : 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 : SAVE International
Publisher :
Page : 145 pages
File Size : 16,87 MB
Release : 2016-05-17
Category : Value analysis (Cost control)
ISBN : 9780996124898
This Function Analysis Guide will give you a greater understanding of Function Analysis to the extent that it becomes second nature to those using the Value Methodology to improve their projects, products, and processes. Application of the techniques covered herein will result in better studies and, most importantly, better results. Lawrence D. Miles, the "Father of Value Analysis," stated "the customer wants a function." People want functions, not things. Function Analysis is considered the heart of the Value Methodology (VM), yet many people have difficulty applying its concepts and techniques to their projects, products, and processes. This document provides guidance on the process and application of function analysis, including Function Analysis System Technique (FAST) for practitioners and those who are preparing to become certified through SAVE International(R).
Author : A. A. Kirillov
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 16,98 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461381533
Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.
Author : Marian Fabian
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 13,65 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 1475734808
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.
Author : Markus Haase
Publisher : American Mathematical Society
Page : 394 pages
File Size : 18,63 MB
Release : 2014-09-17
Category : Mathematics
ISBN : 0821891715
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 : James T. Chok
Publisher : Academic Press
Page : 158 pages
File Size : 31,64 MB
Release : 2019-09-18
Category : Education
ISBN : 0128172134
Functional Analysis: A Practitioner’s Guide to Implementation and Training provides practitioners with the most updated information about applying the wide span of current functional analysis (FA) methodologies geared specifically to applied service settings. The book serves as a self-instructional implementation to a broad-base of trainees and care-providers within schools, clinics, centers and human services organizations. Adopting a Behavioral Skills Training and competency-based training outcomes approach, the learning materials and activities featured in the book include suggested slideshow presentations, role-play exercises, pre- and post-training quizzes, natural setting evaluation methods, data recording forms, instructional scripts and reproducible handouts. Covers an historical overview and the ethical considerations of functional analysis Examines FA methodology, measurement methods and experimental designs Teaches how to independently design, conduct and interpret FAs Explains how to formulate FA-informed intervention plans Presents an agile curriculum that can be customized for different providers
Author : Eberhard Malkowsky
Publisher : CRC Press
Page : 532 pages
File Size : 47,9 MB
Release : 2019-02-25
Category : Mathematics
ISBN : 0429809549
Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research
Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 47,56 MB
Release : 2010-11-02
Category : Mathematics
ISBN : 0387709142
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Author : Orr Moshe Shalit
Publisher : CRC Press
Page : 257 pages
File Size : 38,7 MB
Release : 2017-03-16
Category : Mathematics
ISBN : 1498771629
Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.
Author : Robert J. Zimmer
Publisher : University of Chicago Press
Page : 169 pages
File Size : 46,28 MB
Release : 1990-01-15
Category : Mathematics
ISBN : 0226983382
Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.
