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Fractal Geometry, Complex Dimensions and Zeta Functions Geometry and Spectra of Fractal Strings /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2013.
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| Edición: | 2nd ed. 2013. |
| Colección: | Springer Monographs in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-1-4614-2176-4 | ||
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| 005 | 20220625012838.0 | ||
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| 008 | 120920s2013 xxu| s |||| 0|eng d | ||
| 020 | |a 9781461421764 |9 978-1-4614-2176-4 | ||
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| 100 | 1 | |a Lapidus, Michel L. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Fractal Geometry, Complex Dimensions and Zeta Functions |h [electronic resource] : |b Geometry and Spectra of Fractal Strings / |c by Michel L. Lapidus, Machiel van Frankenhuijsen. |
| 250 | |a 2nd ed. 2013. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2013. | |
| 300 | |a XXVI, 570 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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 researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Key Features include: · The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings · Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra · Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal · Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula · The method of Diophantine approximation is used to study self-similar strings and flows · Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: "The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications." --Nicolae-Adrian Secelean, Zentralblatt. | ||
| 650 | 0 | |a Number theory. | |
| 650 | 0 | |a Measure theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Dynamical systems. | |
| 650 | 0 | |a Global analysis (Mathematics). | |
| 650 | 0 | |a Manifolds (Mathematics). | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Number Theory. |
| 650 | 2 | 4 | |a Measure and Integration. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Dynamical Systems. |
| 650 | 2 | 4 | |a Global Analysis and Analysis on Manifolds. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 700 | 1 | |a van Frankenhuijsen, Machiel. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9781461421757 |
| 776 | 0 | 8 | |i Printed edition: |z 9781461421771 |
| 776 | 0 | 8 | |i Printed edition: |z 9781489988386 |
| 830 | 0 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-1-4614-2176-4 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||