Completeness and Basis Properties of Sets of Special Functions
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Completeness and Basis Properties of Sets of Special Functions by J. R. Higgins
Book DescriptionThis tract presents an exposition of methods for testing sets of special functions for completeness and basis properties, mostly in L2 and L2 spaces. The first chapter contains the theoretical background to the subject, largely in a general Hilbert space setting, and theorems in which the structure of Hilbert space is revealed by properties of its bases are dealt with. Later parts of the book deal with methods: for example, the Vitali criterion, together with its generalisations and applications, is discussed in some detail, and there is an introduction to the theory of stability of bases. The last chapter deals with complete sets as eigenfunctions of differential and a table of a wide variety of bases and complete sets of special functions. Dr Higgins' account will be useful to graduate students of mathematics and professional mathematicians, especially Banach spaces. The emphasis on methods of testing and their applications will also interest scientists and engineers engaged in fields such as the sampling theory of signals in electrical engineering and boundary value problems in mathematical physics.
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Book DetailsISBN: 9780521604888
(216mm x 138mm x 9mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 3-Jun-2004
Country of Publication: United Kingdom
Books By Author J. R. Higgins
Sampling Theory in Fourier and Signal Analysis: Advanced Topics, Hardback (November 1999)
Volume 1 in this series laid the mathematical foundations of sampling theory; Volume 2 surveys the many applications of the theory both within mathematics and in other areas of science. Topics range over a wide variety of areas, and each application is given a modern treatment.
Sampling Theory in Fourier and Signal Analysis: Foundations, Hardback (May 1996)» View all books by J. R. Higgins
This monograph explores the equivalence of signal functions with their sets of values taken at discrete points. Beginning with an introduction to the main ideas, and background material on Fourier analysis and Hilbert spaces and their bases, it covers a wide variety of topics.
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