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Fractal geometry, complex dimensions and zeta functions : geometry and spectra of fractal strings / / Michel L. Lapidus, Machiel van Frankenhuijsen
| Fractal geometry, complex dimensions and zeta functions : geometry and spectra of fractal strings / / Michel L. Lapidus, Machiel van Frankenhuijsen |
| Autore | Lapidus Michel L |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York, : Springer, 2013 |
| Descrizione fisica | 1 online resource (582 p.) |
| Disciplina | 514.742 |
| Altri autori (Persone) | FrankenhuijsenMachiel van |
| Collana | Springer monographs in mathematics |
| Soggetto topico |
Fractals
Functions, Zeta Geometry, Riemannian Number theory |
| ISBN |
1-283-90955-3
1-4614-2176-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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. |
| Record Nr. | UNINA-9910438156403321 |
Lapidus Michel L
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| New York, : Springer, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Fractal zeta functions and fractal drums : higher-dimensional theory of complex dimensions / / by Michel L. Lapidus, Goran Radunović, Darko Žubrinić
| Fractal zeta functions and fractal drums : higher-dimensional theory of complex dimensions / / by Michel L. Lapidus, Goran Radunović, Darko Žubrinić |
| Autore | Lapidus Michel L |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (XL, 655 p. 55 illus., 10 illus. in color.) |
| Disciplina | 512.7 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Number theory
Measure theory Mathematical physics Number Theory Measure and Integration Mathematical Physics |
| ISBN | 3-319-44706-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Overview -- Preface -- List of Figures -- Key Words -- Selected Key Results -- Glossary -- 1. Introduction -- 2 Distance and Tube Zeta Functions -- 3. Applications of Distance and Tube Zeta Functions -- 4. Relative Fractal Drums and Their Complex Dimensions -- 5.Fractal Tube Formulas and Complex Dimensions -- 6. Classification of Fractal Sets and Concluding Comments -- Appendix A. Tame Dirchlet-Type Integrals -- Appendix B. Local Distance Zeta Functions -- Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs -- Acknowledgements -- Bibliography -- Author Index -- Subject Index. . |
| Record Nr. | UNINA-9910254280703321 |
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Lapidus Michel L
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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