TY - JOUR
T1 - Asymptotics for orthogonal polynomials and separation of their zeros
AU - Levin, Eli
AU - Lubinsky, D. S.
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - Let pn denote the orthonormal polynomials associated with a measure μ with compact support on the real line. In a recent paper, we showed there is a close relationship between the spacing of zeros of successive orthogonal polynomials pn,pn−1, and uniform bounds on the orthogonal polynomials in subintervals of the support. In this paper, we show there is also a relationship between asymptotics for the spacing of zeros of pn−1,pn, and pointwise asymptotics for the orthogonal polynomials.
AB - Let pn denote the orthonormal polynomials associated with a measure μ with compact support on the real line. In a recent paper, we showed there is a close relationship between the spacing of zeros of successive orthogonal polynomials pn,pn−1, and uniform bounds on the orthogonal polynomials in subintervals of the support. In this paper, we show there is also a relationship between asymptotics for the spacing of zeros of pn−1,pn, and pointwise asymptotics for the orthogonal polynomials.
KW - Orthogonal polynomials
KW - Pointwise asymptotics
UR - http://www.scopus.com/inward/record.url?scp=85135726479&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2022.105804
DO - 10.1016/j.jat.2022.105804
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AN - SCOPUS:85135726479
SN - 0021-9045
VL - 281
SP - 105804
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
M1 - 105804
ER -