Counting Function Asymptotics and the Weak Weyl-Berry Conjecture for Connected Domains with Fractal Boundaries

作     者：Chen Hua (Department of Mathematics,Wuhan University,Wuhan 430072,China)(Email:chenhua@whu,***)Brian D.Sleeman (School of Mathematics,University of Leeds,Leeds LS2 9JT,England,UK)(Email:bds@amsta.leeds,ac.uk) 

作者机构：Department of Mathematics Wuhan University Wuhan China School of Mathematics University of Leeds Leeds England UK 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1998年第14卷第2期

页      面：261-276页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Research partially supported by the Natural Science Foundation of China and the Royal Society of London 

主　　题：Connected fractal domain Counting function Weyl-Berry conjecture 

摘      要：In this paper,we study the spectral asymptotics for connected fractal domains and Weyl-Berry *** 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 ***,we also study a naturally connected fractal domain,and we prove,in this case,the weak Weyl-Berry conjecture holds as well.