From Classical Analysis To Analysis On Fractals
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From Classical Analysis to Analysis on Fractals
Author: Patricia Alonso Ruiz
language: en
Publisher: Springer Nature
Release Date: 2023-10-24
Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.
Analysis on Fractals
Author: Jun Kigami
language: en
Publisher: Cambridge University Press
Release Date: 2001-06-07
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
Fractals in Probability and Analysis
Author: Christopher J. Bishop
language: en
Publisher: Cambridge University Press
Release Date: 2017
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.