TY - JOUR
T1 - Orthogonal polynomials for weights close to indeterminacy
AU - Levin, E.
AU - Lubinsky, D. S.
PY - 2007/8
Y1 - 2007/8
N2 - We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W : R → [0, ∞) that are 'close' to indeterminate weights. Our main example is exp fenced(- || fenced(x) fenced(log || fenced(x))β), with β real, possibly modified near 0, but our results also apply to exp fenced(- || fenced(x)α fenced(log || fenced(x))β), α < 1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.
AB - We obtain estimates for Christoffel functions and orthogonal polynomials for even weights W : R → [0, ∞) that are 'close' to indeterminate weights. Our main example is exp fenced(- || fenced(x) fenced(log || fenced(x))β), with β real, possibly modified near 0, but our results also apply to exp fenced(- || fenced(x)α fenced(log || fenced(x))β), α < 1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.
UR - https://www.scopus.com/pages/publications/34447645973
U2 - 10.1016/j.jat.2007.01.001
DO - 10.1016/j.jat.2007.01.001
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AN - SCOPUS:34447645973
SN - 0021-9045
VL - 147
SP - 129
EP - 168
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 2
ER -