LEADER 05026nam 2200601 450 001 9910480591203321 005 20170828133252.0 010 $a1-4704-1082-6 035 $a(CKB)3780000000000211 035 $a(EBL)3113246 035 $a(SSID)ssj0001339194 035 $a(PQKBManifestationID)11762084 035 $a(PQKBTitleCode)TC0001339194 035 $a(PQKBWorkID)11349540 035 $a(PQKB)11179611 035 $a(MiAaPQ)EBC3113246 035 $a(PPN)197102441 035 $a(EXLCZ)993780000000000211 100 $a20140612h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFractal geometry and dynamical systems in pure and applied mathematics I $efractals in pure mathematics /$fDavid Carfi [and three others], editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2013. 210 4$dİ2013 215 $a1 online resource (410 p.) 225 1 $aContemporary Mathematics,$x1098-3627 ;$vVolume 600 300 $a"PISRS 2011, First International Conference : Analysis, Fractal Geometry, Dynamical Systems and Economics, November 8-12, 2011, Messina, Sicily, Italy." 300 $a"AMS Special Session, in memory of Benoit Mandelbrot : Fractal Geometry in Pure and Applied Mathematics, January 4-7, 2012, Boston, Massachusetts." 300 $a"AMS Special Session : Geometry and Analysis on Fractal Spaces, March 3-4, 2012, Honolulu, Hawaii." 311 $a0-8218-9147-2 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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 a???_{ }""; ""3.1. A a???heuristica??? definition of _{ }.""; ""3.2. The weighted Hilbert space a???_{ }.""; ""3.3. The infinitesimal shifts a???_{ } and their properties.""; ""3.4. The spectral operator _{ }."" 327 $a""4. Inverse and Direct Spectral Problems for Fractal Strings""""4.1. The original inverse spectral problem.""; ""4.2. Fractal strings and the (modified) Weyla???Berry conjecture.""; ""5. Quasi-Invertibility and Almost Invertibility of the Spectral Operator""; ""5.1. The truncated operators a???^{( )}_{ } and ^{( )}_{ }.""; ""5.2. The spectra of a???_{ }^{( )} and ^{( )}_{ }.""; ""5.3. Quasi-invertibility of _{ }, almost invertibility and Riemann zeroes.""; ""6. Spectral Reformulations of the Riemann Hypothesis and of Almost RH"" 327 $a""6.1. Quasi-invertibility of _{ } and spectral reformulation of RH""""6.2. Almost invertibility of _{ } and spectral reformulation of a???Almost RHa???.""; ""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:Riemanna???s Explicit Formula""; ""9. Appendix B:The Momentum Operator and Normality of a???_{ }""; ""References"" 327 $a""Analysis and Geometry of the Measurable Riemannian Structure on the SierpiA??ski Gasket""""1. Introduction""; ""2. SierpiA??ski gasket and its standard Dirichlet form""; ""3. Measurable Riemannian structure on the SierpiA??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"" 327 $a""7. Weyla???s Laplacian eigenvalue asymptotics"" 410 0$aContemporary mathematics (American Mathematical Society) ;$vVolume 600. 606 $aFractals$vCongresses 608 $aElectronic books. 615 0$aFractals 676 $a514/.742 702 $aCarfi$b David$f1971- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480591203321 996 $aFractal geometry and dynamical systems in pure and applied mathematics I$91938689 997 $aUNINA