Overview
This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Most of the presented material is published here for the first time.
Synopsis
Fractals and Spectra Hans Triebel
This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently.
Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played.
The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated.
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It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time.
- Zentralblatt MATH
(…) the monograph presents in a self-contained and very readable and lively form a new, intriguing and potentially very useful chapter of the theory of pseudodifferential operators.
- Mathematical Reviews
The book deals with a very recent topic and presents the significant contributions of the author. It is directed to mathematicians interested in the interrelations between function spaces and fractal geometry and is also of interest for graduate students.
- Operator Theory Reviews
Booknews
Maps the recently discovered symbiotic relationship among the theory of function spaces, fractal geometry, and the spectral theory of pseudo-differential operators. Begins with a discussion of atomic and quarkonial decompositions in scalar and vector valued function spaces on the Euclidean n-space; then progresses to properties of function spaces on and of fractals. Applies to a fractal setting assertions from earlier work based on sharp estimates of entropy numbers of compact embeddings between function spaces and their relations to the distribution of eigenvalues. Sets out in some detail the techniques used, especially those that have not appeared in the literature before. Annotation c. by Book News, Inc., Portland, Or.