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1. Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
by Michel L. Lapidus, Machiel Frankenhuijsen
出版情報: New York, NY : Springer Science+Business Media, LLC, 2006
シリーズ名: Springer Monographs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-0-387-35208-4
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電子ブック
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2. Ergodic Theory : with a view towards Number Theory
by Manfred Einsiedler, Thomas Ward
出版情報: London : Springer-Verlag London Limited, 2011
シリーズ名: Graduate Texts in Mathematics ; 259
オンライン: http://dx.doi.org/10.1007/978-0-85729-021-2
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電子ブック
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3. Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings. 2nd ed. 2013
by Michel L. Lapidus, Machiel van Frankenhuijsen
出版情報: New York, NY : Springer New York : Imprint: Springer, 2013
シリーズ名: Springer Monographs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-1-4614-2176-4
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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
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4. Geometry and Analysis of Fractals : Hong Kong, December 2012
edited by De-Jun Feng, Ka-Sing Lau
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014
シリーズ名: Springer Proceedings in Mathematics & Statistics ; 88
オンライン: http://dx.doi.org/10.1007/978-3-662-43920-3
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Mandelbrot cascades and related topics
Law of pure types and some exotic spectra of fractal spectral measures
The role of transfer operators and shifts in the study of fractals: encoding-models, analysis and geometry, commutative and non-commutative
Generalized energy inequalities and higher multifractal moments
Some Aspects of Multifractal analysis
Heat kernels on metric measure spaces
Stochastic completeness of jump processes on metric measure spaces
Self similar sets, entropy and additive combinatorics
Quasisymmetric modification of metrics on self-similar sets
Recent progress on dimensions of projections
The geometry of fractal percolation
Self-affine sets and the continuity of subadditive pressure
Stability properties of fractal curvatures
Mandelbrot cascades and related topics
Law of pure types and some exotic spectra of fractal spectral measures
The role of transfer operators and shifts in the study of fractals: encoding-models, analysis and geometry, commutative and non-commutative
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5. Weakly Wandering Sequences in Ergodic Theory
by Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
出版情報: Tokyo : Springer Japan : Imprint: Springer, 2014
シリーズ名: Springer Monographs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-4-431-55108-9
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6. Equidistribution in Number Theory, An Introduction
edited by Andrew Granville, Zeév Rudnick
出版情報: Dordrecht : Springer, 2007
シリーズ名: NATO Science Series ; 237
オンライン: http://dx.doi.org/10.1007/978-1-4020-5404-4
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電子ブック
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7. Substitution Dynamical Systems - Spectral Analysis
by Martine Queffélec
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2010
シリーズ名: Lecture Notes in Mathematics ; 1294
オンライン: http://dx.doi.org/10.1007/978-3-642-11212-6
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