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Walk dimension and function spaces on self-similar fractals. (English) Zbl 1180.60064

MacG. Dawson, Robert J. (ed.) et al., Convex and fractal geometry. Papers of the conference, Będlewo, Poland, May 21–26, 2007. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-03-4/pbk). Banach Center Publications 84, 63-73 (2009).
This article is a short review of the construction of Brownian motion on some self-similar fractals and the associated notions of dimension. Particular attention is given to the relationship of probabilistic versus functional analytic aspects.
For the entire collection see [Zbl 1156.00015].

MSC:

60J35 Transition functions, generators and resolvents
60J65 Brownian motion
28A80 Fractals
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