Fractals and Spectra: Related to Fourier Analysis and Function Spaces - Brossura

Triebel, Hans

Brossura

ISBN 10: 3034800339 ISBN 13: 9783034800334

Casa editrice: Birkhäuser, 2010

Riassunto

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 spectral problems of degenerate n pseudodifferential operators in ? and in bounded domains. Besides a few special properties of function spaces we relied there on sharp estimates of entropy numbers of compact embeddings between these spaces and their relations to the distribution of eigenvalues. Some of the main assertions of the present book are based on just these techniques but now in a fractal setting. Since virtually nothing of these new methods is available in literature, a substantial part of what we have to say deals with recent developments in the theory of function spaces, also for their own sake. In this respect the book might also be considered as a continuation of [Tri83] and [Tri92].

Su questo libro

Informazioni sull?autore

Hans Triebel ist Professor der Mathematik an der Friedrich-Schiller-Universität Jena.

Dalla quarta di copertina

Fractals and SpectraHans TriebelThis 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.------ 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 ReviewsThe 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

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 3034800339
• ISBN 13: 9783034800334
• Rilegatura: Copertina flessibile
• Numero di pagine: 280
• Contatto del produttore: non disponibile
• Persona responsabile: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Germania