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The theme of this work, the logarithmic integral, lies athwart much of twentieth-century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an investigation which explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows. The presentation is straightforward, so that by following the theme, Professor Koosis has produced a work that can be read as a whole. He has brought together here many results, some unpublished, some new, and some available only in inaccessible journals.

Analytic functions. --- Harmonic analysis. --- Integrals, Logarithmic.

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Treated in this volume are selected topics in analytic &Ggr;-almost-periodic functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-periodic structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebr

Analytic functions. --- Function algebras. --- Almost periodic functions. --- Functions, Almost periodic --- Fourier series --- Algebras, Function --- Analytic functions --- Banach algebras --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's

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Analytic functions --- Analytische functies --- Approximatietheorie --- Approximation theory --- Fonctions analytiques --- Fonctions continues --- Functies [Doorlopende ] --- Functions [Continuous ] --- Mathématiques appliquées --- Théorie des approximations --- Toegepaste wiskunde --- Théorie de l'approximation --- Approximation theory. --- Functions, Continuous. --- 517.15 --- Functions, Continuous --- AA / International- internationaal --- 305.976 --- 330.3 --- Continuous functions --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- Asymptotic formulae and expressions --- Algoritmen. Optimisatie. --- Methode in staathuishoudkunde. Statische, dynamische economie. Modellen. Experimental economics. --- 517.15 Asymptotic formulae and expressions --- Théorie de l'approximation --- Algoritmen. Optimisatie --- Methode in staathuishoudkunde. Statische, dynamische economie. Modellen. Experimental economics --- Mathematical analysis.