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Zbl 0645.46024
Young, Nicholas
An introduction to Hilbert space. (English)
[B] Cambridge Mathematical Textbooks. Cambridge (UK) etc.: Cambridge University Press. 239 p. \sterling 9.95/pbk (1988). ISBN 0-521-33717-8/pbk

The present book is intended primarily for an undergraduate audience. The authors believes that a sound grounding in Hilbert space theory is the best way how to approach functional analysis. It consists of sixteen chapters dealing with the following topics: Inner product spaces, Normed spaces, Hilbert and Banach spaces, Orthogonal expansions, Classical Fourier series, Dual spaces, Linear operators, Compact operators, Sturm- Liouville systems, Green's functions, Eigenfunction expansions, Positive operators and contractions, Hardy spaces, Approximation by analytic functions and approximation by meromorphic functions. This last chapter and the one concerning the positive operators may be of interest to electrical engineers, since some recent developments, particularly in control and filter design, require familiarity with this aspect of operator theory. The book presupposes introductory courses in real analysis, linear algebra, topology of metric spaces and elementary complex analysis. The chapter concerning Hardy spaces requires a certain familiarity with Lebesgue measure.
[L.Janos]

MSC 2000:: *46C05 Geometry and topology of inner product spaces
46-01 Textbooks (functional analysis)
46C99 Inner product spaces, Hilbert spaces
47B06 Riesz operators and eigenvalue distributions
34L99 Ordinary differential operators
47B15 Hermitian and normal operators
41A30 Approximation by other special function classes
47A10 Spectrum and resolvent of linear operators
47A70 Eigenfunction expansions of linear operators
46B03 Isomorphic theory (including renorming) of Banach spaces

Keywords: Inner product spaces; Normed spaces; Hilbert and Banach spaces; Orthogonal expansions; Fourier series; Dual spaces; Linear operators; Compact operators; Sturm-Liouville systems; Green's functions; Eigenfunction expansions; Positive operators; contractions; Hardy spaces; Approximation by analytic functions; approximation by meromorphic functions

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