SeminarsThe Weyl Criterion for the Spectrum
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In this talk I prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will use the new criterion to study the variation in the spectrum under continuous perturbations of the operator. In the particular case of the Laplacian on differential k-forms over an open manifold we will use these analytic tools to find significantly stronger results for its spectrum including its behavior under a continuous deformation of the metric of the manifold. This is joint with N. Charalambous.
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Zhiqin Lu
2014-08-25
10:30:00 - 12:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
In this talk I prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will use the new criterion to study the variation in the spectrum under continuous perturbations of the operator. In the particular case of the Laplacian on differential k-forms over an open manifold we will use these analytic tools to find significantly stronger results for its spectrum including its behavior under a continuous deformation of the metric of the manifold. This is joint with N. Charalambous.