To give the really big picture in a paragraph, consider a tree on n vertices. View the vertices
as points in abstract (rather than d-dimensional) space, but let the edges have length (= 1 …

The notes are based on lectures given in St. Flour in 1995, and cover, in greater detail, most
of the course given there. The word" fractal" was coined by Mandelbrot [Man] in the 1970s …

Statistical Methods for Long Term Memory Processes covers the diverse statistical methods
and applications for data with long-range dependence. Presenting material that previously …

This book covers analysis on fractals, a develo** area of mathematics which focuses on
the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a …

The main theme of this book is the interplay between the behaviour of a class of stochastic
processes (random walks) and discrete structure theory. The author considers Markov …

The modeling of stochastic dependence is fundamental for understanding random systems
evolving in time. When measured through linear correlation, many of these systems exhibit a …

We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

Many phenomena in physics and engineering have fractal structures; then analysis on them
has a vital role in the application. In this chapter, we present some frameworks of analysis on …

The main object of this paper is the Laplace operator on a class of fractals. First, we
establish the concept of the renormalization of difference operators on post critically finite …

A harmonic calculus on the Sierpinski spaces Page 1 Japan J, AppL Math., 6 (1989), 259-2,90 A
Harmonic Calculus on the Sierpinski Spaces Jun KIGAMI* Department of Mathematics, Faculty …