Triebels book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. This book paves the way to sharp inequalities and embeddings in function spaces, spectral theory and semi-linear equations.

At the American Chemical Society meeting in Philadelphia, Pennsylvania, U.S.A., a symposium was organized entitled, "Comparison of Ab Initio Quantum Chemistry with Experiment: State-of-the-Art." The intent of the symposium was to bring together forefront experimen talists, who perform the types of clean, penetrating experiments that are amenable to thorough theoretical analysis, with inventive theore ticians who have developed high accuracy ab initio methods that are capable of competing favorably with experiment, to assess the current applicability of theoretical methods in chemistry....

This book may be considered as the continuation of the monographs Tri?]and Tri?] with the same title. It deals with the theory of function spaces of type s s B and F as it stands at the beginning of this century. These two scales of pq pq spacescovermanywell-knownspacesoffunctionsanddistributionssuchasH] older- Zygmundspaces, (fractionalandclassical)Sobolevspaces, BesovspacesandHardy spaces. On the one hand this book is essentially self-contained. On the other hand we concentrate principally on those developments in recent times which are related to the nowadays numerous applications of...

The book deals with the two scales B^s_{p, q} and F^s_{p, q} of spaces of distributions, where -∞n in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart of the book. Chapter 3 deals with corresponding spaces on smooth bounded domains in R_n. These results are applied in Chapter 4 in order to study general boundary value problems for regular elliptic differential operators in the above spaces....

n This book deals with several aspects of fractal geometry in ? which are closely connected with Fourier analysis, function spaces, and appropriate (pseudo)differ- tial operators. It emerged quite recently that some modern techniques in the theory of function spaces are intimately related to methods in fractal geometry. Special attention is paid to spectral properties of fractal (pseudo)differential operators; in particular we shall play the drum with a fractal layer. In some sense this book may be considered as the fractal twin of ET96], where we developed adequate methods to handle...

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.

This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m): m E zn} is a resolution of unity in ]R. n. Let 'IjJ 3(x)...