Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9521151 | Indagationes Mathematicae | 2005 | 11 Pages |
Abstract
Let q â {2, 3} and let 0 = s0 < s1 < ⦠< sq = T be integers. For m, n â Z, we put ¯m,n = {j â Z| m⩽ j ⩽ n}. We set lj = sj â sjâ1 for j â 1, q. Given (p1,, pq) â Rq, let b: Z â R be a periodic function of period T such that b(·) = pj on sjâ1 + 1, sj for each j â 1, q. We study the spectral gaps of the Jacobi operator (Ju)(n) = u(n + 1) + u(n â 1) + b(n)u(n) acting on l2(Z). By [λ2j , λ2jâ1] we denote the jth band of the spectrum of J counted from above for j â 1, T. Suppose that pm â pn for m â n. We prove that the statements (i) and (ii) below are equivalent for λ â R and i â 1, T â 1.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Kazushi Yoshitomi,