Completeness and basis properties of sets of special functions / J. R. HigginsType de document : MonographieCollection : Cambridge tracts in mathematics, 72Langue : anglais.Pays : Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 1977Description : 1 vol. (x-134 p.) ; 22 cmISBN : 9780521213769.ISSN : 0950-6284.Bibliographie : Bibliographie p. 126-129. Index.Sujet MSC : 42A65, Harmonic analysis in one variable, Completeness of sets of functions in one variable harmonic analysis
33-02, Research exposition (monographs, survey articles) pertaining to special functions
33C10, Special functions - Hypergeometric functions, Bessel and Airy functions, cylinder functions, 0F1
33C45, Special functions - Hypergeometric functions, Orthogonal polynomials and functions of hypergeometric typeEn-ligne : Aperçu Google 2004 | MathSciNet
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The author states that some years ago he was in need of data concerning basis properties of sets of special functions and techniques available for examining such properties. A collection of notes on the subject led to the monograph under review. For an understanding of the subject, the reader should have the usual first courses in real variables (including Lebesgue integration) and in complex variables. A knowledge of functional analysis, though helpful, is not required. The subject matter relates to many important topics in both pure and applied mathematics - bases in Banach spaces, orthogonal functions and polynomials, properties of special functions, interpolation and approximation, eigenfunctions and boundary value problems.
There are four chapters. Chapter I is called "Foundations''. Chapter II is devoted to orthogonal sequences while Chapter III concerns nonorthogonal sequences. Chapter IV deals with differential and integral operators.
The appendices contain some supplementary theorems, definitions of special functions and some complete sequences of special functions. There is a bibliography of about sixty items and a subject index. (MathSciNet)
Bibliographie p. 126-129. Index