Geodesic
On the Determination of Free Evolution in the Lax–Phillips Scattering Scheme for Second-Order Operator-Differential Equations
Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 854-861 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents some necessary and sufficient conditions on abstract positive self-adjoint operators $L$ under which the operator-differential equation $u_{tt}=-Lu$ determines a free evolution in the Lax–Phillips scattering scheme. 
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     author = {S. A. Kuzhel},
     title = {On the {Determination} of {Free} {Evolution} in the {Lax{\textendash}Phillips} {Scattering} {Scheme} for {Second-Order} {Operator-Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {854--861},
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S. A. Kuzhel. On the Determination of Free Evolution in the Lax–Phillips Scattering Scheme for Second-Order Operator-Differential Equations. Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 854-861. http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a5/

[1] Laks P., Fillips R., Teoriya rasseyaniya, Mir, M., 1971

[2] Laks P., Fillips R., Teoriya rasseyaniya dlya avtomorfnykh funktsii, Mir, M., 1979

[3] Kuzhel S., “On some properties of abstract wave equation”, Methods of Functional Analysis and Topology, 3:1 (1997), 82–87 | MR

[4] Kuzhel A. V., Kuzhel S. A., Regular extensions of Hermitian operators, VSP, Utrecht, 1998 | Zbl

[5] Khelgason S., Preobrazovanie Radona, Mir, M., 1980

[6] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1966

[7] Kuzhel S. A., “Pro viglyad vkhidnogo ta vikhidnogo pidprostoriv dlya khvilovogo rivnyannya v $\mathbb R^n$”, Ukr. matem. zh., 52:5 (1999), 711–715

[8] Lax P., Phillips R., “Scattering theory for the acoustic equation in an even number of space dimensions”, Indiana Univ. Math. J., 22:2 (1972), 101–134 | DOI | MR | Zbl