Linear Functional Analysis

Buch | Softcover
324 Seiten
2007 | 2nd ed. 2008
Springer London Ltd (Verlag)
978-1-84800-004-9 (ISBN)

Lese- und Medienproben

Linear Functional Analysis - Bryan Rynne, M.A. Youngson
37,44 inkl. MwSt
This leads to di?culties in that, although many of the elementary properties of ?nite-dimensional vector spaces hold in in?nite-dimensional vector spaces, many others do not. Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space.
This book provides an introduction to the ideas and methods of linear fu- tional analysis at a level appropriate to the ?nal year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the t- ory of metric spaces). Part of the development of functional analysis can be traced to attempts to ?nd a suitable framework in which to discuss di?erential and integral equations. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions de?ned on some set. In general, such a v- tor space is in?nite-dimensional. This leads to di?culties in that, although many of the elementary properties of ?nite-dimensional vector spaces hold in in?nite-dimensional vector spaces, many others do not. For example, in general in?nite-dimensionalvectorspacesthereisnoframeworkinwhichtomakesense of analytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now brie?y outline the contents of the book.

Preliminaries.- Normed Spaces.- Inner Product Spaces, Hilbert Spaces.- Linear Operators.- Duality and the Hahn—Banach Theorem.- Linear Operators on Hilbert Spaces.- Compact Operators.- Integral and Differential Equations.- Solutions to Exercises.

Erscheint lt. Verlag 21.12.2007
Reihe/Serie Springer Undergraduate Mathematics Series
Zusatzinfo 6 Illustrations, black and white; X, 324 p. 6 illus.
Verlagsort England
Sprache englisch
Maße 178 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie
ISBN-10 1-84800-004-9 / 1848000049
ISBN-13 978-1-84800-004-9 / 9781848000049
Zustand Neuware
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