Scattering matrix for the wave equation with finite radial potential in the two-dimensional space
- 27 Downloads
Expressions for partial scattering matricesSl(λ) are obtained for all naturall by using Adamyan's result, which establishes a universal relationship between the scattering matrix for the wave equation with finite potential in a even-dimensional space and the characteristic operator function of a special contraction operator, which describes the dissipation of energy from the region of the space containing a scatterer. It is shown that this problem can be reduced to the case ofl=0 for all evenl and to the case ofl=1 for all oddl.
KeywordsCharacteristic Operator Wave Equation Operator Function Contraction Operator Special Contraction
Unable to display preview. Download preview PDF.
- 1.P. Lax and R. S. Phillips,Scattering Theory, Academic Press, New York (1967).Google Scholar
- 2.P. Lax and R. S. Phillips, “Scattering theory for the acoustic equation in an even number of space dimensions,”Indiana Univ. Math. J.,22, 101–134 (1972).Google Scholar
- 3.V. M. Adamyan and D. Z. Arov, “On scattering operators and semigroups of contractions in the Hilbert space,”Dokl. Akad. Nauk SSSR,165, No. 1, 9–12 (1965).Google Scholar
- 4.V. M. Adamyan, “On scattering theory for the wave equations in even-dimensional spaces,”Funkts. Anal. Prilozh.,10, No. 4, 1–8 (1976).Google Scholar
- 5.A. L. Mil'man, “The inverse problem in the acoustic scattering theory for centrally symmetric finite obstacles in the two-dimensional space,”Ukr. Mat. Zh.,42, No. 12, 1649–1657 (1990).Google Scholar
- 6.B. Szökefalvy-Nagy and C. Foias,Analyse Harmonique des Opérateurs de l'Espace de Hilbert, Académiai Kiadô, Paris (1967).Google Scholar