Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals
نویسندگان
چکیده
منابع مشابه
Smooth bumps, a Borel theorem and partitions of unity on p.c.f. fractals.∗
Recent years have seen considerable developments in the theory of analysis on certain fractal sets from both probabilistic and analytic viewpoints [1, 10, 19]. In this theory, either a Dirichlet energy form or a diffusion on the fractal is used to construct a weak Laplacian with respect to an appropriate measure, and thereby to define smooth functions. As a result the Laplacian eigenfunctions a...
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The main reason for introducing smooth structures was to enable us to define smooth functions on manifolds and smooth maps between manifolds. In this chapter we carry out that project. We begin by defining smooth real-valued and vector-valued functions, and then generalize this to smooth maps between manifolds. We then focus our attention for a while on the special case of diffeomorphisms, whic...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04772-7