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...
محفوظ في:
| المؤلفون الرئيسيون: | , |
|---|---|
| التنسيق: | Livre numérique |
| اللغة: | Anglais |
| منشور في: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| الطبعة: | Second edition. |
| سلاسل: | Springer Monographs in Mathematics
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| ملاحظة: |
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 |
| LEADER | 14251nam a22005777a 4500 | ||
|---|---|---|---|
| 001 | 949595 | ||
| 008 | 130325t20XX2013xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN168295873 | ||
| 020 | |a 9781461421764 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.7 | ||
| 084 | |a 11Mxx. 2010 | ||
| 084 | |a 14G10. 2010 | ||
| 084 | |a 28Axx. 2010 | ||
| 084 | |a 35P20. 2010 | ||
| 084 | |a 37Cxx. 2010 | ||
| 084 | |a 58J32. 2000 | ||
| 100 | 1 | |a Lapidus, Michel, |d 1956- | |
| 245 | 1 | 0 | |a Fractal geometry, complex dimensions and zeta functions : |b geometry and spectra of fractal strings |c Michel L. Lapidus, Machiel van Frankenhuijsen. |
| 250 | |a Second edition. | ||
| 256 | |a Données textuelles | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Springer Monographs in Mathematics |x 2196-9922 | |
| 500 | |a Description d'après consultation du 2016-03-04 | ||
| 500 | |a Titre provenant de l'écran d'accueil | ||
| 500 | |a Numérisation de l'édition de New York ; Heidelberg ; London [etc.] : Springer, cop. 2013 | ||
| 500 | |a Nombre de pages de l'édition imprimée : 592 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. 515-547. Notes bibliogr. Index | ||
| 505 | 1 | |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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 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 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 · 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 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 · 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 · 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 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. | ||
| 538 | |a Nécessite un lecteur de fichier PDF | ||
| 650 | |a Fractales | ||
| 650 | |a Fonctions zêta | ||
| 650 | |a Théorie spectrale (mathématiques) | ||
| 650 | |a Nombres, Théorie des | ||
| 700 | 1 | |a Frankenhuijsen, Machiel van, |d 1967- |4 aut | |
| 776 | 0 | |0 165198419 |t Fractal geometry, complex dimensions and zeta functions |o geometry and spectra of fractal strings |f Michel L. Lapidus, Machiel van Frankenhuijsen |e Second edition |c New York |n Springer |d 2013 |p 1 vol. (XXV-567 p.) |s Springer monographs in mathematics |z 978-1-4614-2175-7 | |
| 776 | 0 | |0 165198419 |t Fractal geometry, complex dimensions and zeta functions |o geometry and spectra of fractal strings |f Michel L. Lapidus, Machiel van Frankenhuijsen |e Second edition |c New York |n Springer |d 2013 |p 1 vol. (XXV-567 p.) |s Springer monographs in mathematics |z 978-1-4614-2175-7 | |
| 776 | 0 | |t Fractal Geometry, Complex Dimensions and Zeta Functions |b Texte imprimé |z 9781461421771 | |
| 776 | 0 | |t Fractal Geometry, Complex Dimensions and Zeta Functions |b Texte imprimé |z 9781489988386 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-1-4614-2176-4 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-5K6Q4NWS-8 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:748119639 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-1-4614-2176-4 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:751574201 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-1-4614-2176-4 |z Accès INSA CVL | |
| 997 | |0 949595 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||