Analysis, Probability and Mathematical Physics on Fractals

Analysis, Probability and Mathematical Physics on Fractals（Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications）

分形分析、概率与数学物理
几何学

原价：

￥ 1720.00

售价：

发货周期：预计3-5周发货

作者

Ruiz, Patricia Alonso(编辑)

出版社

World Scientific Publishing

出版时间

2020年02月26日

装帧

精装

ＩＳＢＮ

9789811215520

复制

页码

596

开本

9.02 x 5.98 x 1.25

语种

英文

综合评分

暂无评分

图书详情
目次
买家须知
书评（0）
权威书评（0）

图书简介

In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature? This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results. Key Features: o The book presents the current frontiers in research on analysis, probability and mathematical physics on fractals o The mathematics of fractals is a rapidly developing research area with a large and active community of scientists, many of whom contributed to this volume o The authors include many leading researchers, and the book includes introductory material combined with more advanced topics that should make it accessible to newcomers to the field as well as interesting to experts

A Capacity Approach to Box and Packing Dimensions of Projections and Other Images (K J Falconer); Minkowski Measurability Criteria for Compact Sets and Relative Fractal Drums in Euclidean Spaces (Michel L Lapidus, Goran Radunović and Darko Žubrinić); Orthonormal Coalescence Hidden-Variable Fractal Interpolation Functions (G P Kapoor and Srijanani Anurag Prasad); Fractal Transformed Doubly Reflected Brownian Motions (Tim Ehnes and Uta Freiberg); Harmonic Analysis of Fractal Measures: Basis and Frame Algorithms for Fractal L²-Spaces, and Boundary Representations as Closed Subspaces of the Hardy Space (John E Herr, Palle E T Jorgensen and Eric S Weber); Spectral Pairs and Positive-Definite-Tempered Distributions (Palle E T Jorgensen and Feng Tian); Asymptotic Behavior of Jacobi Matrices of IFS: A Long-Standing Conjecture (Giorgio Mantica); Random Walks and Induced Dirichlet Forms on Compact Spaces of Homogeneous Type (Shi-Lei Kong, Ka-Sing Lau and Ting-Kam Leonard Wong); Analysis on the Projective Octagasket (Yiran Mao, Robert S Strichartz, Levente Szabo and Wing Hong Wong); Measures Essentially of Finite Type and Spectral Asymptotics of Fractal Laplacians (Sze-Man Ngai); Eigenvalue Approximation for Krein–Feller-Operators (Uta Freiberg and Lenon Minorics); Spectral Asymptotics on the Hanoi Attractor (Elias Hauser); Sobolev Spaces and Calculus of Variations on Fractals (Michael Hinz, Dorina Koch and Melissa Meinert); Approximation of Magnetic Laplacians on the Sierpinski Gasket by Discrete Magnetic Laplacians (Olaf Post and Jan Simmer); Magnetostatic Problems in Fractal Domains (Simone Creo, Maria Rosaria Lancia, Paola Vernole, Michael Hinz and Alexander Teplyaev); Infinite Propagation Speed for Wave Solutions on Some Post-critically Finite Fractals (Yin Tat Lee); The Damped Stochastic Wave Equation on Post-critically Finite Fractals (Ben Hambly and Weiye Yang); Fractal AC Circuits and Propagating Waves on Fractals (Eric Akkermans, Joe P Chen, Gerald Dunne, Luke G Rogers and Alexander Teplyaev);

Trade Policy 买家须知