Abstract
In this paper, we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture. We prove, for some special connected fractal domains, the sharp estimate for second term of counting function asymptotics, which implies that the weak form of the Weyl-Berry conjecture holds for the case. Finally, we also study a naturally connected fractal domain, and we prove, in this case, the weak Weyl-Berry conjecture holds as well.
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Research partially supported by the Natural Science Foundation of China-and the Royal Society of London
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Hua, C., Sleeman, B.D. Counting function asymptotics and the weak Weyl-Berry conjecture for connected domains with fractal boundaries. Acta Mathematica Sinica 14, 261–276 (1998). https://doi.org/10.1007/BF02560212
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DOI: https://doi.org/10.1007/BF02560212