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 -