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Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet

Abstract:
We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpiñski carpets. For all these functions the leading term is of the form xγφ(log x) for a suitable exponent γ and φ a periodic function. We also discuss similar results for the heat content of affine nested fractals. © Canadian Mathematical Society 2010.
Publication status:
Published

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Publisher copy:
10.4153/CJM-2010-079-7

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Volume:
63
Issue:
1
Pages:
153-180
Publication date:
2011-02-05
DOI:
EISSN:
1496-4279
ISSN:
0008-414X
URN:
uuid:c8f8e615-b551-4273-bf06-68158c5a6c7d
Source identifiers:
120299
Local pid:
pubs:120299
Language:
English

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