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

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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. 
@article{MZM_2000_68_6_a5,
     author = {S. A. Kuzhel},
     title = {On the {Determination} of {Free} {Evolution} in the {Lax--Phillips} {Scattering} {Scheme} for {Second-Order} {Operator-Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {854--861},
     publisher = {mathdoc},
     volume = {68},
     number = {6},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a5/}
}
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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/