Orthogonal Polynomials with Recursion Coefficients of Generalized Bounded Variation
نویسندگان
چکیده
منابع مشابه
Orthogonal Polynomials with Recursion Coefficients of Generalized Bounded Variation
n=0 |eiφlβ n+1 − β n | <∞ for some φl ∈ R. This includes discrete Schrödinger operators on a half-line or line with finite linear combinations of Wigner–von Neumann potentials cos(nφ+α)/n , where γ > 0. For the real line, our results state that in the Lebesgue decomposition dμ = fdm+ dμs of such measures, supp(dμs) ∩ (−2, 2) is contained in an explicite finite set S (thus, dμ has no singular co...
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We review recent results on necessary and sufficient conditions for measures on R and ∂D to yield exponential decay of the recursion coefficients of the corresponding orthogonal polynomials. We include results on the relation of detailed asymptotics of the recursion coefficients to detailed analyticity of the measures. We present an analog of Carmona’s formula for OPRL. A major role is played b...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2011
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-011-1287-9