The Structure of Functions

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 authors book \Fractals and Spectra\ (MMA 91). It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and in particular how they are interrelated.