Fractal Zeta Functions and Fractal Drums Higher-Dimensional Theory of Complex Dimensions /

• Main Authors: Lapidus, Michel L. (Author), Radunović, Goran (Author), Žubrinić, Darko (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Measure theory.; Number theory.; Mathematical physics.; Number Theory.; Measure and Integration.; Mathematical Physics.

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...

Table of 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. .