Some counterexamples to subexponential growth of orthogonal polynomials
Studia Mathematica (1995)
- Volume: 116, Issue: 2, page 197-206
- ISSN: 0039-3223
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Abstract
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topZygmunt, Marcin. "Some counterexamples to subexponential growth of orthogonal polynomials." Studia Mathematica 116.2 (1995): 197-206. <http://eudml.org/doc/216227>.
@article{Zygmunt1995,
abstract = {We give examples of polynomials p(n) orthonormal with respect to a measure μ on ⨍ such that the sequence \{p(n,x)\} has exponential lower bound for some points x of supp μ. Moreover, the set of such points is dense in the support of μ.},
author = {Zygmunt, Marcin},
journal = {Studia Mathematica},
keywords = {orthogonal polynomials; recurrence formula; subexponential growth; exponential growth; perturbations},
language = {eng},
number = {2},
pages = {197-206},
title = {Some counterexamples to subexponential growth of orthogonal polynomials},
url = {http://eudml.org/doc/216227},
volume = {116},
year = {1995},
}
TY - JOUR
AU - Zygmunt, Marcin
TI - Some counterexamples to subexponential growth of orthogonal polynomials
JO - Studia Mathematica
PY - 1995
VL - 116
IS - 2
SP - 197
EP - 206
AB - We give examples of polynomials p(n) orthonormal with respect to a measure μ on ⨍ such that the sequence {p(n,x)} has exponential lower bound for some points x of supp μ. Moreover, the set of such points is dense in the support of μ.
LA - eng
KW - orthogonal polynomials; recurrence formula; subexponential growth; exponential growth; perturbations
UR - http://eudml.org/doc/216227
ER -
References
top- [1] D. S. Lubinsky and P. Nevai, Sub-exponential growth of solutions of difference equations, J. London Math. Soc. 46 (1992), 149-160. Zbl0723.39003
- [2] P. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 213 (1979).
- [3] P. Nevai, V. Totik, and J. Zhang, Orthogonal polynomials: their growth relative to their sums, J. Approx. Theory 67 (1991), 215-234. Zbl0754.42013
- [4] R. Szwarc, Counterexample to subexponential growth of orthogonal polynomials, Constr. Approx., to appear. Zbl0852.42013
- [5] J. Zhang, Relative growth of linear iteration and orthogonal polynomials on several intervals, Linear Algebra Appl. 186 (1993), 97-115. Zbl0769.41006
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