Geodesic
Spectral analysis of a nonselfadjoint differential operator arising in the one-dimensional problem of scattering by a Brownian particle
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 371-390 Cet article a éte moissonné depuis la source Math-Net.Ru

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The operator $H=-\partial_{xx}+i\varkappa\partial_{yy}+q(x-y)\cdot$ arising in the averaging of a solution of the Schrödinger equation with a random time-dependent potential is investigated. Analysis of the operator reduces to the study of a family of one-dimensional operators $$ B_p=-\frac{d^2}{dx^2}+2p\frac d{dx}+\frac{q(x)}{1-i\varkappa},\qquad p\in\mathbf R. $$ The distribution of the discrete and continuous spectra of the operators $B_p$ and $H$ is studied. An expansion in eigenfunctions of the operators $B_p$ in $L_2(\mathbf R)$ for almost all $p$ and of the operator $H$ on a set dense in $L_2(\mathbf R^2)$ is obtained. Figures: 1. Bibliography: 4 titles. 
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     author = {S. E. Cheremshantsev},
     title = {Spectral analysis of a~nonselfadjoint differential operator arising in the one-dimensional problem of scattering by {a~Brownian} particle},
     journal = {Sbornik. Mathematics},
     pages = {371--390},
     year = {1987},
     volume = {57},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_57_2_a2/}
}
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S. E. Cheremshantsev. Spectral analysis of a nonselfadjoint differential operator arising in the one-dimensional problem of scattering by a Brownian particle. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 371-390. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a2/

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