Appendix to Functional Analysis
Author | : Frigyes Riesz |
Publisher | : |
Total Pages | : |
Release | : |
Genre | : |
ISBN | : |
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Author | : Frigyes Riesz |
Publisher | : |
Total Pages | : |
Release | : |
Genre | : |
ISBN | : |
Author | : Frigyes Riesz |
Publisher | : |
Total Pages | : |
Release | : 1960 |
Genre | : |
ISBN | : |
Author | : Markus Haase |
Publisher | : American Mathematical Society |
Total Pages | : 394 |
Release | : 2014-09-17 |
Genre | : 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 | : Theo Bühler |
Publisher | : American Mathematical Soc. |
Total Pages | : 482 |
Release | : 2018-08-08 |
Genre | : Mathematics |
ISBN | : 147044190X |
It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.
Author | : Martin Schechter |
Publisher | : American Mathematical Soc. |
Total Pages | : 450 |
Release | : 2001-11-13 |
Genre | : Mathematics |
ISBN | : 0821828959 |
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 | : Frigyes Riesz |
Publisher | : |
Total Pages | : 36 |
Release | : 1960 |
Genre | : Functional analysis |
ISBN | : |
In 2007, the U.S. Department of Labor (DOL) and the U.S. Department of Defense (DoD) began a joint initiative to support the spouses of military personnel in their pursuit of portable postsecondary degrees or industry-recognized credentials. Through the Military Spouse Career Advancement Account (CAA) Demonstration, eligible spouses could obtain an account to pay for career-related education and training. Demonstration goals were to (1) help military spouses with careers and (2) encourage the retention of service members by increasing families' satisfaction with military life. Eight states received demonstration grants, which were used in substate areas where participating military bases and One-Stop Career Centers were located. DOL and DoD established demonstration guidelines about the local partnerships to be formed; which military spouses were eligible for CAAs; the types of training, education, and credentials that could be funded; the funding amount available to each spouse; and the extent of guidance that demonstration staff could give to spouses.) This report presents findings from the implementation evaluation of the Military Spouse Career Advancement Account Demonstration. Part I: Early Implementation of the Military Spouse Career Advancement Accounts Demonstration provides an overview of the demonstration and key findings about the demonstration's partnerships, early implementation experiences, marketing efforts, and other topics. Part II: Additional Findings from the Military Spouse Career Advancement Accounts Demonstration Study supplements the earlier report by providing additional information on implementation issues and quantitative information about the characteristics of participants, as well as their plans for using the CAAs for participation in education and training programs and the attainment of credentials, licenses, or certifications to support careers in high-wage, high-growth occupations.).
Author | : Peter D. Lax |
Publisher | : John Wiley & Sons |
Total Pages | : 451 |
Release | : 2014-08-28 |
Genre | : Mathematics |
ISBN | : 1118626745 |
Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. Includes an appendix on the Riesz representation theorem.
Author | : Frigyes Riesz |
Publisher | : |
Total Pages | : |
Release | : 1955 |
Genre | : |
ISBN | : |
Author | : Robert J. Zimmer |
Publisher | : University of Chicago Press |
Total Pages | : 169 |
Release | : 1990-01-15 |
Genre | : 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.
Author | : Béla Szökefalvi-Nagy |
Publisher | : |
Total Pages | : 36 |
Release | : 1960 |
Genre | : Functional analysis |
ISBN | : |