Metrics, fractals, operators..., 25 Feb 2003
Fractals make headlines from time to time[--are they everywhere?], and and they make beautiful color pictures; but they are also part of a substantial mathematical theory, even one with an exciting mathematical history. This lovely book presents the subject elegantly in a way that it can be taught to students. It starts with the basics, then systematically, step by step, it builds up the central results. Great for the classrom, or for selfstudy! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. Example: By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. Compared to other books at the same level, for example, by Falconer, 1990, and the equally attractive one from 1985[The geometry of fractal sets], Kigami's book stresses the analysis of the Laplace operator. Falconer covers the theory more generally, and his books have a slightly more potential theoretic bent.