This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.and was shown in [LaMa2] to have a positive answer for fractal strings whose dimension is c a (0, 1) a {1 2 } if and only if the Riemann hypothesis is true. ... the Riemann hypothesis is obtained from a rigorous operator theoretic point of view, thereby further extending the earlier work ... a visiting professor in the Spring of 2012 while this paper was written. c2013 American Mathematical Society Contents 1.

Title | : | Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics |

Author | : | David Carfi, Michel Laurent Lapidus, Erin P. J. Pearse, Machiel Van Frankenhuysen |

Publisher | : | American Mathematical Soc. - 2013-10-22 |

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