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Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials. / Korotyaev, Evgeny; Kutsenko, Anton.
в: Communications in Mathematical Physics, Том 261, № 3, 02.2006, стр. 673-692.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials
AU - Korotyaev, Evgeny
AU - Kutsenko, Anton
PY - 2006/2
Y1 - 2006/2
N2 - Consider the discrete 1D Schrödinger operator on ℤ with an odd 2k periodic potential q. For small potentials we show that the mapping: q→ heights of vertical slits on the quasi-momentum domain (similar to the Marchenko-Ostrovski maping for the Hill operator) is a local isomorphism and the isospectral set consists of 2 k distinct potentials. Finally, the asymptotics of the spectrum are determined as q→0.
AB - Consider the discrete 1D Schrödinger operator on ℤ with an odd 2k periodic potential q. For small potentials we show that the mapping: q→ heights of vertical slits on the quasi-momentum domain (similar to the Marchenko-Ostrovski maping for the Hill operator) is a local isomorphism and the isospectral set consists of 2 k distinct potentials. Finally, the asymptotics of the spectrum are determined as q→0.
UR - http://www.scopus.com/inward/record.url?scp=29144461963&partnerID=8YFLogxK
U2 - 10.1007/s00220-005-1429-z
DO - 10.1007/s00220-005-1429-z
M3 - Article
AN - SCOPUS:29144461963
VL - 261
SP - 673
EP - 692
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 3
ER -
ID: 86257234