Displaying similar documents to “A trace formula for resonances and application to semi-classical Schrödinger operators”

Asymptotic behaviour of the scattering phase for non-trapping obstacles

Veselin Petkov, Georgi Popov (1982)

Annales de l'institut Fourier

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Let S ( λ ) be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle 𝒪 ⊂ R n , n ≥ 3 with Dirichlet or Neumann boundary conditions on ∂ 𝒪 . The function s ( λ ) , called scattering phase, is determined from the equality e - 2 π i s ( λ ) = det S ( λ ) . We show that s ( λ ) has an asymptotic expansion s ( λ ) ∼ ∑ j = 0 ∞ c j λ n - j as λ → + ∞ and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.