منابع مشابه
Algebraic spectral gaps
For the one-dimensional Schrödinger equation, some real intervals with no eigenvalues (the spectral gaps) may be obtained rather systematically with a method proposed by H. Giacomini and A. Mouchet in 2007. The present article provides some alternative formulation of this method, suggests some possible generalizations and extensively discusses the higher-dimensional case. H. Giacomini et A. Mou...
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H-fields are ordered differential fields that capture some basic properties of Hardy fields and fields of transseries. Each H-field is equipped with a convex valuation, and solving first-order linear differential equations in Hfield extensions is strongly affected by the presence of a “gap” in the value group. We construct a real closed H-field that solves every first-order linear differential ...
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Suppose that S ⊆ Fp, where p is a prime number. Let λ1, ..., λp be the Fourier coefficients of S arranged as follows |Ŝ(0)| = |λ1| ≥ |λ2| ≥ · · · ≥ |λp|. Then, as is well known, the smaller |λ2| is, relative to |λ1|, the larger the sumset S +S must be; and, one can work out as a function of ε and the density θ = |S|/p, an upper bound for the ratio |λ2|/|λ1| needed in order to guarantee that S +...
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Motivated by the analysis of Schrödinger operators with periodic potentials we consider the following abstract situation: Let ∆X be the Laplacian on a non-compact Riemannian covering manifold X with a discrete isometric group Γ acting on it such that the quotient X/Γ is a compact manifold. We prove the existence of a finite number of spectral gaps for the operator ∆X associated with a suitable ...
متن کاملComparison of Metric Spectral Gaps
Let A = (aij) ∈ Mn(R) be an n by n symmetric stochastic matrix. For p ∈ [1,∞) and a metric space (X, dX), let γ(A, dpX) be the infimum over those γ ∈ (0,∞] for which every x1, . . . , xn ∈ X satisfy 1 n2 n ∑
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ژورنال
عنوان ژورنال: ESAIM: Proceedings
سال: 2012
ISSN: 1270-900X
DOI: 10.1051/proc/201235009