Synopses & Reviews
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. - - -
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.
About the Author
Hans Triebel was professor of mathematics at the Friedrich-Schiller-University Jena, Germany.
Table of Contents
Preface.- I Decompositions of Functions.- II Sharp Inequalities.- III Fractal Elliptic Operators.- IV Truncations and Semi-linear Equations.- References.- Symbols.- Index.