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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

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