Displaying similar documents to “On non-overdetermined inverse scattering at zero energy in three dimensions”

Scattering length and capacity

M. Kac, J. M. Luttinger (1975)

Annales de l'institut Fourier

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An expression in terms of the Wiener integral for the “scattering length” is given and used to discuss the relation between this quantity and electrostatic capacity.

Norm estimates of discrete Schrödinger operators

Ryszard Szwarc (1998)

Colloquium Mathematicae

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Harper’s operator is defined on ℓ 2 ( Z ) by H θ ξ ( n ) = ξ ( n + 1 ) + ξ ( n - 1 ) + 2 cos n θ ξ ( n ) , where θ ∈ [ 0 , π ] . We show that the norm of ∥ H θ ∥ is less than or equal to 2 2 for π / 2 ≤ θ ≤ π . This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.

Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits

Didier Robert, H. Tamura (1989)

Annales de l'institut Fourier

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We study the semi-classical asymptotic behavior as ( h → 0 ) of scattering amplitudes for Schrödinger operators - ( 1 / 2 ) h 2 Δ + V . The asymptotic formula is obtained for energies fixed in a non-trapping energy range and also is applied to study the low energy behavior of scattering amplitudes for a certain class of slowly decreasing repulsive potentials without spherical symmetry.