Geodesic
Trace formulas for resonances
Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 439-447

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For the dissipative operator that arises in the problem of resonance scattering of plane waves by a one-dimensional crystal the first trace formula is obtained and a way of obtaining the others is indicated. The high-energy asymptotic behavior of the reflection coefficient is found as well. 
@article{TMF_1983_56_3_a10,
     author = {A. V. Rybkin},
     title = {Trace formulas for resonances},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {439--447},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a10/}
}
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A. V. Rybkin. Trace formulas for resonances. Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 439-447. http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a10/