Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Spectral estimates for a periodic fourth-order operator. / Badanin, A. V.; Korotyaev, E. L.
в: St. Petersburg Mathematical Journal, Том 22, № 5, 01.12.2011, стр. 703-736.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Spectral estimates for a periodic fourth-order operator
AU - Badanin, A. V.
AU - Korotyaev, E. L.
PY - 2011/12/1
Y1 - 2011/12/1
N2 - The operator H = d4/dt4 + d/dtpd/dt +q with periodic coefficients p, q on the real line is considered. The spectrum of H is absolutely continuous and consists of intervals separated by gaps. The following statements are proved: 1) the endpoints of gaps are periodic or antiperiodic eigenvalues or branch points of the Lyapunov function, and moreover, their asymptotic behavior at high energy is found; 2) the spectrum of H at high energy has multiplicity two; 3) if p belongs to a certain class, then for any q the spectrum of H has infinitely many gaps, and all branch points of the Lyapunov function, except for a finite number of them, are real and negative; 4) if q = 0 and p → 0, then at the beginning of the spectrum there is a small spectral band of multiplicity 4, and its asymptotic behavior is found; the remaining spectrum has multiplicity 2.
AB - The operator H = d4/dt4 + d/dtpd/dt +q with periodic coefficients p, q on the real line is considered. The spectrum of H is absolutely continuous and consists of intervals separated by gaps. The following statements are proved: 1) the endpoints of gaps are periodic or antiperiodic eigenvalues or branch points of the Lyapunov function, and moreover, their asymptotic behavior at high energy is found; 2) the spectrum of H at high energy has multiplicity two; 3) if p belongs to a certain class, then for any q the spectrum of H has infinitely many gaps, and all branch points of the Lyapunov function, except for a finite number of them, are real and negative; 4) if q = 0 and p → 0, then at the beginning of the spectrum there is a small spectral band of multiplicity 4, and its asymptotic behavior is found; the remaining spectrum has multiplicity 2.
KW - Periodic differential operator
KW - Spectral asymptotics
KW - Spectral bands
UR - http://www.scopus.com/inward/record.url?scp=84858263427&partnerID=8YFLogxK
U2 - 10.1090/S1061-0022-2011-01164-1
DO - 10.1090/S1061-0022-2011-01164-1
M3 - Article
VL - 22
SP - 703
EP - 736
JO - St. Petersburg Mathematical Journal
JF - St. Petersburg Mathematical Journal
SN - 1061-0022
IS - 5
ER -
ID: 5288278