Operators with singular continuous spectrum, V. Sparse potentials
نویسندگان
چکیده
منابع مشابه
Operators with Singular Continuous Spectrum, v. Sparse Potentials
By presenting simple theorems for the absence of positive eigenvalues for certain one-dimensional Schrödinger operators, we are able to construct explicit potentials which yield purely singular continuous spectrum. §
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§0. Introduction The Baire category theorem implies that the family, F , of dense sets Gδ in a fixed metric space, X, is a candidate for generic sets since it is closed under countable intersections; and if X is perfect (has no isolated point), then A ∈ F has uncountable intersections with any open ball in X. There is a long tradition of soft arguments to prove that certain surprising sets are ...
متن کاملOperators with Singular Continuous Spectrum: Iii. Almost Periodic Schrödinger Operators
We prove that one-dimensional Schrödinger operators with even almost periodic potential have no point spectrum for a dense Gδ in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense Gδ in θ even if the frequency is an irrational with good Diophantine properties. §
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1996
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-96-03465-x