Linear Functional Analysis

Author: Bryan Rynne
Publisher: Springer Science & Business Media
ISBN: 1848000057
Release Date: 2007-12-29
Genre: Mathematics

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. A highlight of the second edition is a new chapter on the Hahn-Banach theorem and its applications to the theory of duality.

Metric Spaces

Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
ISBN: 1846286271
Release Date: 2006-12-26
Genre: Mathematics

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

Linear Functional Analysis for Scientists and Engineers

Author: Balmohan V. Limaye
Publisher: Springer
ISBN: 9789811009723
Release Date: 2016-06-18
Genre: Mathematics

This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance structure of a metric space, functional analysis is increasingly gaining the attention of not only mathematicians but also scientists and engineers. The purpose of the text is to present the basic aspects of functional analysis to this varied audience, keeping in mind the considerations of applicability. A novelty of this book is the inclusion of a result by Zabreiko, which states that every countably subadditive seminorm on a Banach space is continuous. Several major theorems in functional analysis are easy consequences of this result. The entire book can be used as a textbook for an introductory course in functional analysis without having to make any specific selection from the topics presented here. Basic notions in the setting of a metric space are defined in terms of sequences. These include total boundedness, compactness, continuity and uniform continuity. Offering concise and to-the-point treatment of each topic in the framework of a normed space and of an inner product space, the book represents a valuable resource for advanced undergraduate students in mathematics, and will also appeal to graduate students and faculty in the natural sciences and engineering. The book is accessible to anyone who is familiar with linear algebra and real analysis.

Basic Methods of Linear Functional Analysis

Author: John D. Pryce
Publisher: Courier Corporation
ISBN: 9780486173634
Release Date: 2014-05-05
Genre: Mathematics

Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973 edition.

Regression

Author: N. H. Bingham
Publisher: Springer Science & Business Media
ISBN: 1848829698
Release Date: 2010-09-17
Genre: Mathematics

Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential. Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions. The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh’s Probability Models, and T. S. Blyth & E.F. Robertsons’ Basic Linear Algebra and Further Linear Algebra.

Calculus of One Variable

Author: K.E. Hirst
Publisher: Springer Science & Business Media
ISBN: 9781846282225
Release Date: 2006-01-27
Genre: Mathematics

Adopts a user-friendly approach, with an emphasis on worked examples and exercises, rather than abstract theory The computer algebra and graphical package MAPLE is used to illustrate many of the ideas and provides an additional aid to teaching and learning Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web

Beginning Functional Analysis

Author: Karen Saxe
Publisher: Springer Science & Business Media
ISBN: 9781475736878
Release Date: 2013-04-17
Genre: Mathematics

The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts.

Measure Integral and Probability

Author: Marek Capinski
Publisher: Springer Science & Business Media
ISBN: 9781447136316
Release Date: 2013-06-29
Genre: Mathematics

This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

Elements of Abstract Analysis

Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
ISBN: 9781447101796
Release Date: 2012-12-06
Genre: Mathematics

While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.

Elementary Functional Analysis

Author: Barbara MacCluer
Publisher: Springer Science & Business Media
ISBN: 9780387855295
Release Date: 2008-10-20
Genre: Mathematics

Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A.M. Vershik ([45], p. 438). This text evolved from the content of a one semester introductory course in fu- tional analysis that I have taught a number of times since 1996 at the University of Virginia. My students have included ?rst and second year graduate students prep- ing for thesis work in analysis, algebra, or topology, graduate students in various departments in the School of Engineering and Applied Science, and several und- graduate mathematics or physics majors. After a ?rst draft of the manuscript was completed, it was also used for an independent reading course for several und- graduates preparing for graduate school.

Sturm Liouville Theory and its Applications

Author: M. A. Al-Gwaiz
Publisher: Springer Science & Business Media
ISBN: 9781846289712
Release Date: 2008-01-15
Genre: Mathematics

Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The text’s presentation follows a clear, rigorous mathematical style that is highly readable. The author first establishes the basic results of Sturm-Liouville theory and then provides examples and applications to illustrate the theory. The final two chapters, on Fourier and Laplace transformations, demonstrate the use of the Fourier series method for representing functions to integral representations.

A Course in Functional Analysis

Author: John B. Conway
Publisher: Springer Science & Business Media
ISBN: 9781475738285
Release Date: 2013-04-17
Genre: Mathematics

Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.

Fundamentals of Functional Analysis

Author: Douglas Farenick
Publisher: Springer
ISBN: 9783319456331
Release Date: 2016-10-24
Genre: Mathematics

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.

Linear Functional Analysis

Author: Hans Wilhelm Alt
Publisher: Springer
ISBN: 9781447172802
Release Date: 2016-07-06
Genre: Mathematics

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.