Displaying similar documents to “A formula for the eigenvalues of a compact operator”

Spectral asymptotics for manifolds with cylindrical ends

Tanya Christiansen, Maciej Zworski (1995)

Annales de l'institut Fourier

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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.

On the characterization of scalar type spectral operators

P. A. Cojuhari, A. M. Gomilko (2008)

Studia Mathematica

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The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.