# Search Results for "functional-analysis"

## Functional Analysis

**Author**: Yurij M. Berezansky,Zinovij G. Sheftel,Georgij F. Us**Publisher:**Birkhäuser**ISBN:**3034891857**Category:**Mathematics**Page:**426**View:**5729

"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.

## Functional Analysis I

*Linear Functional Analysis*

**Author**: Yu.I. Lyubich**Publisher:**Springer Science & Business Media**ISBN:**3662028492**Category:**Mathematics**Page:**286**View:**1720

The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.

## Functional Analysis

**Author**: E. Suhubi**Publisher:**Springer Science & Business Media**ISBN:**9401701415**Category:**Mathematics**Page:**691**View:**4585

Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.

## Functional Analysis

**Author**: N.A**Publisher:**Academic Press**ISBN:**9780080873978**Category:**Mathematics**Page:**165**View:**6662

Functional Analysis

## Functional Analysis

**Author**: Erdogan Suhubi**Publisher:**Springer Science & Business Media**ISBN:**9781402016165**Category:**Mathematics**Page:**691**View:**5558

Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.

## Elements of functional analysis

**Author**: Aldric Loughman Brown,A. Page**Publisher:**N.A**ISBN:**N.A**Category:**Mathematics**Page:**394**View:**9199

## Nonstandard Methods in Functional Analysis

*Lectures and Notes*

**Author**: Siu-Ah Ng**Publisher:**World Scientific**ISBN:**9814287555**Category:**Mathematics**Page:**340**View:**751

In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz'' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg''s invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.

## Foundations of Functional Analysis

**Author**: S. Ponnusamy**Publisher:**CRC Press**ISBN:**9780849317170**Category:**Mathematics**Page:**457**View:**7674

Foundations of Functional Analysis provides fundamental concepts about the theory and application of various methods involving functional analysis. Part one covers basic facts of linear algebra and real analysis. Part two is devoted to the theory of normed spaces, Banach spaces, contraction mappings, and linear operators between normed spaces. Part three focuses on Hilbert spaces and the representation of continuous linear functional with some applications. In this self-contained book, all the concepts, results, and their consequences are motivated and illustrated by numerous examples in each chapter with carefully chosen exercises.

## Functional Analysis

*Entering Hilbert Space*

**Author**: Vagn Lundsgaard Hansen**Publisher:**World Scientific**ISBN:**9812565639**Category:**Mathematics**Page:**136**View:**4486

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e. , the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo? logical Spaces, Measure Spaces and Linear Spaces. Then, starting with the chapter on Semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions of S. L. SoBOLEV and L. ScmVARTZ. While the book is primarily addressed to graduate students, it is hoped it might prove useful to research mathe? maticians, both pure and applied. The reader may pass e. g. from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integ-ration of the Equation of Evolution). Such materials as 'Weak Topologies and Duality in Locally Convex Spaces' and 'Nuclear Spaces' are presented in the form of the appendices to Chapter V and Chapter X, respectively. These might be skipped for the first reading by those who are interested rather in the application of linear operators.

## Principles of Functional Analysis

**Author**: Martin Schechter**Publisher:**American Mathematical Soc.**ISBN:**0821828959**Category:**Mathematics**Page:**425**View:**771

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.