scholarly journals On Selberg's small eigenvalue conjecture and residual eigenvalues

2011 ◽  
Vol 2011 (656) ◽  
Author(s):  
Morten S. Risager
Keyword(s):  
Small Eigenvalue

Eigenvalue pinching for Riemannian vector bundles

1999 ◽  
Vol 1999 (511) ◽  
pp. 73-86 ◽  
Author(s):  
Peter Petersen ◽  
Chadwick Sprouse
Keyword(s):  
Riemannian Manifold ◽  
Vector Bundle ◽  
Vector Bundles ◽  
Compact Riemannian Manifold ◽  
Small Eigenvalue

Abstract We investigate some very general pinching results for eigensections with small eigenvalue of a Riemannian vector bundle. In particular, this gives pinching results for the eigenvalues of 1-forms on a compact Riemannian manifold, along with other applications.

scholarly journals Infinite Kirchhoff plate on a compact elastic foundation may have arbitrary small eigenvalue

2019 ◽  
Vol 488 (4) ◽  
pp. 362-366
Author(s):  
S. A. Nazarov
Keyword(s):  
Continuous Spectrum ◽  
Neumann Problem ◽  
Elastic Foundation ◽  
Laplace Operator ◽  
Small Eigenvalue ◽  
Winkler Foundation ◽  
Infinite Strip ◽  
Compliance Coefficient ◽  
Strip Waveguide ◽  
The Laplace Operator

An inhomogeneous Kirhhoff plate composed from semi-infinite strip-waveguide and a compaсt resonator which is in contact with the Winkler foundation of small compliance, is considered. It is shown that for any 0, it is possible to find the compliance coefficient O(2) such that the described plate possesses the eigenvalue 4embedded into continuous spectrum. This result is quite surprising because in an acoustic waveguide (the spectral Neumann problem for the Laplace operator) a small eigenvalue does not exist for any unsubstantial perturbation. A reason of this dissension is explained as well.

scholarly journals Small eigenvalue variation and real rank zero

1996 ◽  
Vol 175 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Ola Bratteli ◽  
George Elliott
Keyword(s):  
Small Eigenvalue ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero
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