The Structure of Functions

ISBN-13: 9783034805681 / Angielski / Miękka / 2012 / 425 str.

Hans Triebel

Opis

Dealing with the constructive Weierstrassian approach to the theory of function spaces and its various applications, this volume combines the advantages of atomic and wavelet representations to enhanced theories in spectral fractal elliptics and semi-linear equations.

Spis treści

Preface.- I Decompositions of Functions.- II Sharp Inequalities.- III Fractal Elliptic Operators.- IV Truncations and Semi-linear Equations.- References.- Symbols.- Index.​

O autorze

Hans Triebel was professor of mathematics at the Friedrich-Schiller-University Jena, Germany.

Blurb

This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations.

The book is self-contained, although some parts may be considered as a continuation of the author's book Fractals and Spectra. It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated.

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The book under review can be regarded as a continuation of [his book on "Fractals and spectra", 1997] (...) There are many sections named: comments, preparations, motivations, discussions and so on. These parts of the book seem to be very interesting and valuable. They help the reader to deal with the main course.
(Mathematical Reviews)