Overview
- beginning at the advanced graduate level
- The exposition is gentle with numerous instructive examples and illustrations
- The book builds on the one-dimensional theory of complex dimensions (the case of fractal strings) and builds towards as well as achieves a higher-dimensional theory of complex dimensions for arbitrary compact subsets of Euclidean spaces of any dimension
- The content is self-contained and relatively easily accessible to a wide variety of readers with different levels of mathematical maturity
Part of the book series: Springer Monographs in Mathematics (SMM)
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About this book
The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field.
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Table of contents (6 chapters)
Authors and Affiliations
Bibliographic Information
Book Title: Fractal Zeta Functions and Fractal Drums
Book Subtitle: Higher-Dimensional Theory of Complex Dimensions
Authors: Michel L. Lapidus, Goran Radunović, Darko Žubrinić
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-44706-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2017
Hardcover ISBN: 978-3-319-44704-9Published: 26 June 2017
Softcover ISBN: 978-3-319-83115-2Published: 28 July 2018
eBook ISBN: 978-3-319-44706-3Published: 07 June 2017
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XL, 655
Number of Illustrations: 45 b/w illustrations, 10 illustrations in colour
Topics: Number Theory, Measure and Integration, Mathematical Physics