Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0861.58047
Shima, Tadashi
On eigenvalue problems for Laplacians on p.c.f. self-similar sets. (English)
[J] Japan J. Ind. Appl. Math. 13, No.1, 1-23 (1996). ISSN 0916-7005; ISSN 1868-937X/e

This paper considers a strong harmonic structure under which eigenvalues of the Laplacian on a p.c.f. self-similar set are completely determined according to the dynamical system generated by a rational function. The author shows that, with some additional assumptions, the eigenvalue counting function $\rho(\lambda)$ behaves so wildly that $\rho(\lambda)$ does not vary regularly, and the ratio $\rho(\lambda)/\lambda^{d_s/2}$ is bounded but not convergent as $\lambda \nearrow \infty$, where $d_s$ is the spectral dimension of the p.c.f. self-similar set.
[S.Nikčević (Beograd)]

MSC 2000:: *58J50 Spectral problems; spectral geometry; scattering theory
37A30 Ergodic theorems, spectral theory, Markov operators

Keywords: eigenvalue; post critically finite self-similar sets; spectral decimation; spectral dimension; Laplacian

Cited in: Zbl 1177.28029

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]