Completeness (Cambridge Tracts in Mathematics). Higgins 9780521604888 New<|

Completeness and Basis Properties of Sets of Special FunctionsAuthor(s): J. R. Higgins\nFormat: Paperback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521604888, 978-0521604888\nSynopsis\nThis 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 function.