05026nam 2200601 450 991048059120332120170828133252.01-4704-1082-6(CKB)3780000000000211(EBL)3113246(SSID)ssj0001339194(PQKBManifestationID)11762084(PQKBTitleCode)TC0001339194(PQKBWorkID)11349540(PQKB)11179611(MiAaPQ)EBC3113246(PPN)197102441(EXLCZ)99378000000000021120140612h20132013 uy 0engur|n|---|||||txtccrFractal geometry and dynamical systems in pure and applied mathematics I fractals in pure mathematics /David Carfi [and three others], editorsProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (410 p.)Contemporary Mathematics,1098-3627 ;Volume 600"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."0-8218-9147-2 Includes bibliographical references.""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 â€œAlmost 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. Weylâ€?s Laplacian eigenvalue asymptotics""Contemporary mathematics (American Mathematical Society) ;Volume 600.FractalsCongressesElectronic books.Fractals514/.742Carfi David1971-MiAaPQMiAaPQMiAaPQBOOK9910480591203321Fractal geometry and dynamical systems in pure and applied mathematics I1938689UNINA