Analysis on fractals

Known as: Calculus on fractals

Analysis on fractals or calculus on fractals is a generalization of calculus on smooth manifolds to calculus on fractals. The theory describes…

Papers overview

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2019

The recent field of analysis on fractals has been studied under a probabilistic and analytic point of view. In this present work…

2017

Fractal geometry is the study of sets which exhibit the same pattern at multiple scales. Developing tools to study these sets is…

2017

We discuss several open problems related to analysis on fractals: estimates of the Green functions, the growth rates of the…

2017

On fractals, different measures (mutually singular in general) are involved to measure volumes of sets and energies of functions…

2015

Naturally fractured reservoirs (NFRs) are complex fractured network that have been associated to fractal structures. There are…

2010

Research on analysis on fractals first came from J. Kigami[2][7] and R.Strichartz[3][5][8], the harmonic matrices[2] and the…

2008

Various origins of linear and nonlinear Schrödinger equations are discussed in connection with diffusion, hydrodynamics, and…

2007

This thesis consists of an introduction and a summary, followed by two papers, both of them on the topic of function spaces on…

2006

Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which…

2001

Introduction 1. Geometry of self-similar sets 2. Analysis on limits of networks 3. Construction of Laplacians on P. C. F. self…