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...
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| Hlavní autoři: | , |
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| Médium: | Livre numérique |
| Jazyk: | Anglais |
| Vydáno: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Vydání: | Second edition. |
| Edice: | Springer Monographs in Mathematics
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| Témata: | |
| On-line přístup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Poznámka: |
Description d'après consultation du 2016-03-04 Titre provenant de l'écran d'accueil Numérisation de l'édition de New York ; Heidelberg ; London [etc.] : Springer, cop. 2013 Nombre de pages de l'édition imprimée : 592 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Fractal geometry, complex dimensions and zeta functions, geometry and spectra of fractal strings, Michel L. Lapidus, Machiel van Frankenhuijsen, Second edition, New York, Springer, 2013, 1 vol. (XXV-567 p.), Springer monographs in mathematics, 978-1-4614-2175-7 • Fractal geometry, complex dimensions and zeta functions, geometry and spectra of fractal strings, Michel L. Lapidus, Machiel van Frankenhuijsen, Second edition, New York, Springer, 2013, 1 vol. (XXV-567 p.), Springer monographs in mathematics, 978-1-4614-2175-7 • Fractal Geometry, Complex Dimensions and Zeta Functions, Texte imprimé, 9781461421771 • Fractal Geometry, Complex Dimensions and Zeta Functions, Texte imprimé, 9781489988386 |
Obsah:
- 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