Geodesic
On the~absence of eigenvalues of the~difference Schr\"odinger operator on a~line with a~periodic potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 450-458

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We discuss the difference Schrödinger operator on a line with a periodic, possibly complex, potential. We show that this operator has no eigenvalues. The proof is based on the use of the notion of Bloch solutions introduced by Buslaev and Fedotov for difference equations on a line.
Keywords: Schrödinger operator, difference equation on a line, periodic potential, eigenvalues. 
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     author = {A. A. Fedotov},
     title = {On the~absence of eigenvalues of the~difference {Schr\"odinger} operator on a~line with a~periodic potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {450--458},
     publisher = {mathdoc},
     volume = {213},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a3/}
}
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A. A. Fedotov. On the~absence of eigenvalues of the~difference Schr\"odinger operator on a~line with a~periodic potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 450-458. http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a3/