Levitin, M and Vassiliev, D (1996) Spectral asymptotics, renewal theorem, and the Berry conjecture for a class of fractals. P LOND MATH SOC , 72 188 - 214.
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We consider the asymptotic behaviour of the volume of the Minkowski sausage, the counting function of the Dirichlet Laplacian, the partition function and the heat content for an iterated set G subset of R(m) with fractal boundary. We show, using the renewal theory (well known in probability) that in all cases the asymptotic behaviour depends essentially on whether the set of logarithms of the similitudes used in the construction of G is arithmetic.
|Title:||Spectral asymptotics, renewal theorem, and the Berry conjecture for a class of fractals|
|Keywords:||SELF-SIMILAR MEASURES, FOURIER-TRANSFORMS, POLYGONAL BOUNDARY, 2-TERM ASYMPTOTICS, COUNTING FUNCTION, HEAT-FLOW, DRUM, EIGENVALUES, LAPLACIAN, OPERATORS|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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