منابع مشابه
Institute for Mathematical Physics Inverse Problem and the Trace Formula for the Hill Operator, Ii Inverse Problem and the Trace Formula for the Hill Operator, Ii
Consider the Hill operator T = ?d 2 =dx 2 + q(x) on L 2 (R); where q 2 L 2 (0; 1) is a 1-periodic real potential and R 1 0 q(x)dx = 0: The spectrum of T is absolutely continuous and consists of intervals separated by gaps n = (a ? n ; a
متن کاملThe Uniform Estimates for the Hill
Let G n = (A ? n ; A + n); n 1; be gaps and let n = A ? n?1 ; A + n ] be spectral bands of the Hill operator T = ?d 2 =dx 2 + V (x) in L 2 (R), where V is a 1-periodic real potential from L 2 (0; 1). Let the gap length L n = jG n j; h n be a height of the corresponding slit in the quasimomentum domain and let n = 2 (2n ? 1) ? j n j > 0 be the band reduction.
متن کاملThe Second Order Estimates for the Hill Operatore
Let H be the Hill operator and let G n = (A ? n ; A + n) and M n ; n 1; be the corresponding gaps and the eeective masses for the Hill operator. Denote by F(E) the Lyapunov function for the Hill operator. Let n 2 A ? n ; A + n ] be such that F 0 (n) = 0 and h n 0 be the solution of the equation cosh h n = (?1) n F(n): We prove some identities for the eeective masses M n : Then we nd "second ord...
متن کاملWeighted Estimates for the Averaging Integral Operator
Let 1 < p ≤ q < +∞ and let v, w be weights on (0,+∞) satisfying: (?) v(x)xis equivalent to a non-decreasing function on (0,+∞) for some ρ ≥ 0; [w(x)x] ≈ [v(x)x] for all x ∈ (0,+∞). We prove that if the averaging operator (Af)(x) := 1 x R x 0 f(t) dt, x ∈ (0,+∞), is bounded from the weighted Lebesgue space Lp((0,+∞); v) into the weighted Lebesgue space Lq((0,+∞);w), then there exists ε0 ∈ (0, p−...
متن کاملA priori estimates for the Hill and Dirac operators
Consider the Hill operator Ty = −y′′ + q′(t)y in L2(R), where q ∈ L2(0, 1) is a 1periodic real potential. The spectrum of T is is absolutely continuous and consists of bands separated by gaps γn, n > 1 with length |γn| > 0. We obtain a priori estimates of the gap lengths, effective masses, action variables for the KDV. For example, if μn are the effective masses associated with the gap γn = (λ ...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2006
ISSN: 0022-0396
DOI: 10.1016/j.jde.2005.04.017