Fractal Geometry, Complex Dimensions and Zeta Functions Geometry and Spectra of Fractal Strings /

• Κύριοι συγγραφείς: Lapidus, Michel L. (Συγγραφέας), van Frankenhuijsen, Machiel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2013.
• Έκδοση: 2nd ed. 2013.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Functional analysis.; Global analysis (Mathematics).; Manifolds (Mathematics).; Measure theory.; Partial differential equations.; Number theory.; Number Theory.; Measure and Integration.; Partial Differential Equations.; Dynamical Systems and Ergodic Theory.; Global Analysis and Analysis on Manifolds.; Functional Analysis.

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings; that is, one-dimensional drums with fractal boundary. This second edition of Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researc...

Πίνακας περιεχομένων:

• Preface
• Overview
• Introduction
• 1. Complex Dimensions of Ordinary Fractal Strings
• 2. Complex Dimensions of Self-Similar Fractal Strings
• 3. Complex Dimensions of Nonlattice Self-Similar Strings
• 4. Generalized Fractal Strings Viewed as Measures
• 5. Explicit Formulas for Generalized Fractal Strings
• 6. The Geometry and the Spectrum of Fractal Strings
• 7. Periodic Orbits of Self-Similar Flows
• 8. Fractal Tube Formulas
• 9. Riemann Hypothesis and Inverse Spectral Problems
• 10. Generalized Cantor Strings and their Oscillations
• 11. Critical Zero of Zeta Functions
• 12 Fractality and Complex Dimensions
• 13. Recent Results and Perspectives
• Appendix A. Zeta Functions in Number Theory
• Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics
• Appendix C. An Application of Nevanlinna Theory
• Bibliography
• Author Index
• Subject Index
• Index of Symbols
• Conventions
• Acknowledgements.