Geodesic
Wave operators for the linearized Boltzmann equation in one-speed transport theory
Sbornik. Mathematics, Tome 192 (2001) no. 1, pp. 141-162

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A dissipative integro-differential operator $L$ arising in the linearization of Boltzmann's equation in one-speed particle transport theory is considered. Under assumptions ensuring that the point spectrum of $L$ is finite a scalar multiple of the characteristic functions of $L$ is found and a condition for the absence of spectral singularities is indicated. Using the techniques of non-stationary scattering theory and the Sz.-Nagy–Foias functional model direct and inverse wave operators with the completeness property are constructed. The structure of the operator $L$ in the invariant subspace corresponding to its continuous spectrum is studied. 
@article{SM_2001_192_1_a6,
     author = {S. A. Stepin},
     title = {Wave operators for the linearized {Boltzmann} equation in one-speed transport theory},
     journal = {Sbornik. Mathematics},
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     volume = {192},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_1_a6/}
}
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S. A. Stepin. Wave operators for the linearized Boltzmann equation in one-speed transport theory. Sbornik. Mathematics, Tome 192 (2001) no. 1, pp. 141-162. http://geodesic.mathdoc.fr/item/SM_2001_192_1_a6/