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Fractal zeta functions and fractal drums : higher-dimensional theory of complex dimensions

Author: Michel L Lapidus; Goran Radunović; Darko Žubrinić
Publisher: Cham, Switzerland : Springer, 2017.
Series: Springer monographs in mathematics
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lapidus, Michel L. (Michel Laurent), 1956-
Fractal zeta functions and fractal drums.
Cham, Switzerland : Springer, 2017
(OCoLC)953709319
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michel L Lapidus; Goran Radunović; Darko Žubrinić
ISBN: 9783319447063 3319447068
OCLC Number: 990265562
Description: 1 online resource (xl, 655 pages) : illustrations (some color).
Contents: Overview --
Preface --
List of Figures --
Key Words --
Selected Key Results --
Glossary --
1. Introduction --
2 Distance and Tube Zeta Functions --
3. Applications of Distance and Tube Zeta Functions --
4. Relative Fractal Drums and Their Complex Dimensions --
5. Fractal Tube Formulas and Complex Dimensions --
6. Classification of Fractal Sets and Concluding Comments --
Appendix A. Tame Dirchlet-Type Integrals --
Appendix B. Local Distance Zeta Functions --
Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs --
Acknowledgements --
Bibliography --
Author Index --
Subject Index.
Series Title: Springer monographs in mathematics
Responsibility: Michel L. Lapidus, Goran Radunović, Darko Žubrinić.

Abstract:

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as  Read more...

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