Vai al contenuto principale della pagina
Titolo: | Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / / David Carfi [and three others], editors |
Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
©2013 | |
Descrizione fisica: | 1 online resource (410 p.) |
Disciplina: | 514/.742 |
Soggetto topico: | Fractals |
Soggetto genere / forma: | Electronic books. |
Persona (resp. second.): | CarfiDavid <1971-> |
Note generali: | "PISRS 2011, First International Conference : Analysis, Fractal Geometry, Dynamical Systems and Economics, November 8-12, 2011, Messina, Sicily, Italy." |
"AMS Special Session, in memory of Benoit Mandelbrot : Fractal Geometry in Pure and Applied Mathematics, January 4-7, 2012, Boston, Massachusetts." | |
"AMS Special Session : Geometry and Analysis on Fractal Spaces, March 3-4, 2012, Honolulu, Hawaii." | |
Nota di bibliografia: | Includes bibliographical references. |
Nota di contenuto: | ""Preface""; ""Separation Conditions for Iterated Function Systems with Overlaps""; ""1. Introduction""; ""2. Preliminaries""; ""3. The finite type condition""; ""4. More on the finite type condition""; ""5. Generalized finite type condition""; ""6. Weak separation condition""; ""References""; "" -point Configurations of Discrete Self-Similar Sets""; ""1. Introduction""; ""2. Lower bounds for -point configurations of compatible fractals""; ""3. Determinant fractal zeta functions""; ""References"" |
""Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator""""1. Introduction""; ""2. Generalized Fractal Strings and Their Complex Dimensions""; ""2.1. The geometry and spectra of ordinary fractal strings.""; ""2.2. Generalized fractal strings and their explicit formulas.""; ""3. The Spectral Operator _{ } and the Infinitesimal Shifts â??_{ }""; ""3.1. A â€?heuristicâ€? definition of _{ }.""; ""3.2. The weighted Hilbert space â??_{ }.""; ""3.3. The infinitesimal shifts â??_{ } and their properties.""; ""3.4. The spectral operator _{ }."" | |
""4. Inverse and Direct Spectral Problems for Fractal Strings""""4.1. The original inverse spectral problem.""; ""4.2. Fractal strings and the (modified) Weylâ€?Berry conjecture.""; ""5. Quasi-Invertibility and Almost Invertibility of the Spectral Operator""; ""5.1. The truncated operators â??^{( )}_{ } and ^{( )}_{ }.""; ""5.2. The spectra of â??_{ }^{( )} and ^{( )}_{ }.""; ""5.3. Quasi-invertibility of _{ }, almost invertibility and Riemann zeroes.""; ""6. Spectral Reformulations of the Riemann Hypothesis and of Almost RH"" | |
""6.1. Quasi-invertibility of _{ } and spectral reformulation of RH""""6.2. Almost invertibility of _{ } and spectral reformulation of “Almost RHâ€?.""; ""6.3. Invertibility of the spectral operator and phase transitions.""; ""7. Concluding Comments""; ""7.1. Extension to arithmetic zeta functions.""; ""7.2. Operator-valued Euler products.""; ""7.3. Global spectral operator.""; ""7.4. Towards a quantization of number theory.""; ""8. Appendix A:Riemannâ€?s Explicit Formula""; ""9. Appendix B:The Momentum Operator and Normality of â??_{ }""; ""References"" | |
""Analysis and Geometry of the Measurable Riemannian Structure on the SierpiÅ?ski Gasket""""1. Introduction""; ""2. SierpiÅ?ski gasket and its standard Dirichlet form""; ""3. Measurable Riemannian structure on the SierpiÅ?ski gasket""; ""4. Geometry under the measurable Riemannian structure""; ""5. Short time asymptotics of the heat kernels""; ""5.1. Intricsic metrics and off-diagonal Gaussian behavior""; ""5.2. One-dimensional asymptotics at vertices""; ""5.3. On-diagonal asymptotics at almost every point""; ""6. Ahlfors regularity and singularity of Hausdorff measure"" | |
""7. Weyl�s Laplacian eigenvalue asymptotics"" | |
Titolo autorizzato: | Fractal geometry and dynamical systems in pure and applied mathematics I |
ISBN: | 1-4704-1082-6 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910480591203321 |
Lo trovi qui: | Univ. Federico II |
Opac: | Controlla la disponibilità qui |