Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum
نویسندگان
چکیده
منابع مشابه
Modified Prüfer and Efgp Transforms and Deterministic Models with Dense Point Spectrum
We provide a new proof of the theorem of Simon and Zhu that in the region |E| < λ for a.e. energies, − d2 dx2 + λ cos(xα), 0 < α < 1 has Lyapunov behavior with a quasi-classical formula for the Lyapunov exponent. We also prove Lyapunov behavior for a.e. E ∈ [−2, 2] for the discrete model with V (j2) = ej , V (n) = 0 if n / ∈ {1, 4, 9, . . . }. The arguments depend on a direct analysis of the eq...
متن کاملModified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators
Using control of the growth of the transfer matrices, we discuss the spectral analysis of continuum and discrete half-line Schrödinger operators with slowly decaying potentials. Among our results we show if V (x) = ∑∞ n=1 anW (x − xn), where W has compact support and xn/xn+1 → 0, then H has purely a.c. (resp. purely s.c.) spectrum on (0, ∞) if ∑ an < ∞ (resp. ∑ an = ∞). For λn−1/2an potentials,...
متن کاملSome Schrödinger Operators with Dense Point Spectrum
Given any sequence {En}n−1 of positive energies and any monotone function g(r) on (0,∞) with g(0) = 1, lim r→∞ g(r) = ∞, we can find a potential V (x) on (−∞,∞) so that {En}n=1 are eigenvalues of − d 2 dx2 + V (x) and |V (x)| ≤ (|x| + 1)−1g(|x|). In [7], Naboko proved the following: Theorem 1. Let {κn}∞n=1 be a sequence of rationally independent positive reals. Let g(r) be a monotone function o...
متن کاملSome Jacobi Matrices with Decaying Potential and Dense Point Spectrum
We discuss doubly infinite matrices of the form Mi — δi + 1 -\-δί ._ t + Ff<5i;. as operators on / 2 . We present for each 8>0, examples of potentials Vn with \Vn\ = O(n~ ί/2 + ) and where M has only point spectrum. Our discussion should be viewed as a remark on the recent work of Delyon, Kunz, and Souillard.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1998
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3192