Displaying similar documents to “On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering.”

Asymptotic analysis of non-self-adjoint Hill operators

Oktay Veliev (2013)

Open Mathematics

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We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically...

The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

Borisova, Galina (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12 In this work we present the operators Aγ = γA + -γA with Re γ = 1/2 in the case of an operator A from the class of nondissipative operators generating nonselfadjoint curves, whose correlation functions have a limit as t → ±∞. The asympthotics of the stationary curves e^(itAγ)f as t → ±∞ onto the absolutely continuous subspace of Aγ are obtained. These asymptotics and the obtained asymptotics in [9] of...