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  3. Completeness and Basis Properties of Sets of Special Functions
  • Cited by 112
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1977
Online ISBN:
9780511566189
DOI:
https://doi.org/10.1017/CBO9780511566189
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
Cambridge Tracts in Mathematics (72)
Information

Book description

This 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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