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

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Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings. 2nd ed. 2013

種類:

電子ブック

責任表示:

by Michel L. Lapidus, Machiel van Frankenhuijsen

出版情報:

New York, NY : Springer New York : Imprint: Springer, 2013

著者名:

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9781461421764 [1461421764]

ローカル注記:

学内専用E-BOOKS (local access only)

オンライン

http://dx.doi.org/10.1007/978-1-4614-2176-4

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詳細

主題:

Dynamical Systems and Ergodic Theory; Functional Analysis; Global Analysis and Analysis on Manifolds; Mathematics; Measure and Integration; Number Theory; Partial Differential Equations

分類・件名:

DC23 : 512.7
LCSH : Mathematics
LCSH : Differentiable dynamical systems
LCSH : Functional analysis
LCSH : Global analysis
LCSH : Differential equations, partial
LCSH : Number theory
FREE : Mathematics
FREE : Number Theory
FREE : Measure and Integration
FREE : Partial Differential Equations
FREE : Dynamical Systems and Ergodic Theory
FREE : Global Analysis and Analysis on Manifolds
FREE : Functional Analysis

形態:

XXVI, 567 p. 73 illus : digital

目次情報:

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

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

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書誌ID:

KB00010015

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目次情報

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