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

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Lapidus, Michel L. (Autor), van Frankenhuijsen, Machiel (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2013.
Edición:2nd ed. 2013.
Colección:Springer Monographs in Mathematics,
Temas:
Number theory.
Measure theory.
Differential equations.
Dynamical systems.
Global analysis (Mathematics).
Manifolds (Mathematics).
Functional analysis.
Number Theory.
Measure and Integration.
Differential Equations.
Dynamical Systems.
Global Analysis and Analysis on Manifolds.
Functional Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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