Some counterexamples to subexponential growth of orthogonal polynomials

• Autorzy: Marcin J. Zygmunt
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

orthogonal polynomials; recurrence formula; subexponential growth

Kategorie tematyczne

• 47B39: Difference operators
• 42C05: Orthogonal functions and polynomials, general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 116
• Numer: 2
• Strony: 197-206

Daty

wydano

1995

otrzymano

1995-05-04

Twórcy

autor

Marcin J. Zygmunt

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] D. S. Lubinsky and P. Nevai, Sub-exponential growth of solutions of difference equations, J. London Math. Soc. 46 (1992), 149-160.
• [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.
• [4] R. Szwarc, Counterexample to subexponential growth of orthogonal polynomials, Constr. Approx., to appear.
• [5] J. Zhang, Relative growth of linear iteration and orthogonal polynomials on several intervals, Linear Algebra Appl. 186 (1993), 97-115.