COUNTING FUNCTION ASYMPTOTICS AND THE WEAK WEYL-BERRY CONJECTURE FOR CONNECTED DOMAINS WITH FRACTAL BOUNDARIES

Authors
CHEN H SLEEMAN BD
Citation
H. Chen et Bd. Sleeman, COUNTING FUNCTION ASYMPTOTICS AND THE WEAK WEYL-BERRY CONJECTURE FOR CONNECTED DOMAINS WITH FRACTAL BOUNDARIES, Acta Mathematica Sinica, New Series, 14(2), 1998, pp. 261-276
Citations number
32
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
Journal title
Acta Mathematica Sinica, New Series
ISSN journal
10009574 → ACNP
Volume
14
Issue
2
Year of publication
1998
Pages
261 - 276
Database
ISI
SICI code
1000-9574(1998)14:2<261:CFAATW>2.0.ZU;2-R
Abstract
In this paper, we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture. We prove, for some special connect ed fractal domains, the sharp estimate for second term of counting fun ction asymptotics, which implies that the weak form of the Weyl-Berry conjecture holds for the case. Finally, we also study a naturally conn ected fractal domain, and we prove, in this case, the weak Weyl-Berry conjecture holds as well.