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Can I read Spectral asymptotics for Laplacians on self-similar sets on EtoBox?
Spectral asymptotics for Laplacians on self-similar sets by Naotaka Kajino is a Mathematics article available to read on EtoBox.
What is Spectral asymptotics for Laplacians on self-similar sets about?
Given a self-similar Dirichlet form on a self-similar set, we first give an estimate on the asymptotic order of the associated eigenvalue counting function in terms of a 'geometric counting function' defined through a family of coverings of the self-similar set naturally associated with the Dirichlet space. Secondly, under (sub-)Gaussian heat kernel upper bound, we prove a detailed short time asymptotic behavior of the partition function, which is the Laplace-Stieltjes transform of the eigenvalue counting function associated with the Dirichlet form. This result can be applicable to a class of infinitely ramified self-similar sets including generalized Sierpinski carpets, and is an extension of the result given recently by B.M. Hambly for the Brownian motion on generalized Sierpinski carpets. Moreover, we also provide a sharp remainder estimate for the short time asymptotic behavior of the partition function.
Who reads Spectral asymptotics for Laplacians on self-similar sets?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Naotaka Kajino
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)
- Published
- 2010
- Language
- EN
- Field
- Mathematics (Physical Sciences)