# 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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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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