On the determination of free evolution in the Lax-Phillips scattering scheme for second-order operator-differential equations

Mathematical Notes

Volumn 68, Issue 5-6, 2000, Pages 724-729

  Kuzhel, S A ^a  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

Author keywords

Free evolution; Laplacian; Lax Phillips scattering scheme; Nonperturbed operator; Wave equation

Indexed keywords

EID: 28644448398     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1026604515376     Document Type: Article

References (8)

1. P. Lax and R. Phillips, Scattering Theory, Academic Press, New York (1967).
2. P. Lax and R. Phillips, Scattering Theory for Automorphic Functions, Van Nostrand, Princeton (1976).
3. S. Kuzhel, "On some properties of abstract wave equation," Methods of Functional Analysis and Topology, 3, No. 1, 82-87 (1997).
4. A. V. Kuzhel and S. A. Kuzhel, Regular extensions of Hermitian operators, VSP, Utrecht (1998).
5. S. Helgason, The Radon Transformation, Birkhäuser, Boston (1980).
6. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in the Hilbert Space [in Russian], Nauka, Moscow (1966).
7. S. A. Kuzhel', "On the structure of the incoming and outgoing subspaces for the wave equation in Rn," Ukrain. Mat. Zh. [Ukrainian Math. J.], 52, No. 5, 711-715 (1999).
8. P. Lax and R. Phillips, "Scattering theory for the acoustic equation in an even number of space dimensions," Indiana Univ. Math. J., 22, No. 2, 101-134 (1972).