TY - JOUR

T1 - Spectral asymptotics, renewal theorem, and the Berry conjecture for a class of fractals

AU - Levitin, Michael

AU - Vassiliev, Dmitri

PY - 1996/1

Y1 - 1996/1

N2 - 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 script G sign ? Rm 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 script G sign is arithmetic.

AB - 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 script G sign ? Rm 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 script G sign is arithmetic.

UR - http://www.scopus.com/inward/record.url?scp=33747018374&partnerID=8YFLogxK

U2 - 10.1112/plms/s3-72.1.188

DO - 10.1112/plms/s3-72.1.188

M3 - Article

SN - 0024-6115

VL - 72

SP - 188

EP - 214

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 1

ER -