SPECTRAL ASYMPTOTICS FOR MANIFOLDS WITH CYLINDRICAL ENDS

被引：29

作者：

CHRISTIANSEN, T ^{[1
]}

ZWORSKI, M ^{[1
]}

机构：

[1] JOHNS HOPKINS UNIV,DEPT MATH,BALTIMORE,MD 21218

来源：

ANNALES DE L INSTITUT FOURIER | 1995年 / 45卷 / 01期

关键词：

EIGENVALUES; SCATTERING PHASE; MANIFOLDS WITH CYLINDRICAL ENDS;

D O I：

10.5802/aif.1455

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to r(2), O(r(n)), where n is the dimension of the manifold.

引用

页码：251 / 263

页数：13

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