Geodesic
Invariance principle for generalized wave operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 1, pp. 49-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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In a Hilbert space $\mathfrak H$ a study is made of limits of the form $W_{\pm}(H,H_0|\Lambda)=\displaystyle\operatornamewithlimits{s-lim}_{t\to\pm\infty}\exp\{it H\}\Lambda(t)$ it being assumed that $\varphi(H)W_{\pm}=W_{\pm}\varphi(H_0)$ for any function $\varphi$ that the operators $H$ and $H_0$ are selfadjoint, and that $\Lambda(t)$ is bounded. The invariance principle states that the limit $\displaystyle\operatornamewithlimits{s-lim}_{t\to\pm\infty}\exp\{if(H,t)\}Q(\varphi,t)$, where $Q$ is a certain operator constructed explicitly from $\Lambda$ and $f$, is independent of the choice of $f$ and is identical with $W_{\pm}(H,H_0|\Lambda)$. In some cases the invariance principle can be justified by invoking a theorem proved in the paper. Applications of this theorem to the Schrödinger equation are considered. 
@article{TMF_1971_8_1_a4,
     author = {V. B. Matveev},
     title = {Invariance principle for generalized wave operators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {49--54},
     year = {1971},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_8_1_a4/}
}
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V. B. Matveev. Invariance principle for generalized wave operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 1, pp. 49-54. http://geodesic.mathdoc.fr/item/TMF_1971_8_1_a4/

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