What parts of a measure's support attract zeros of the corresponding orthogonal polynomials?

Authors:
E. B. Saff and Vilmos Totik

Journal:
Proc. Amer. Math. Soc. **114** (1992), 185-190

MSC:
Primary 42C05; Secondary 30C99

DOI:
https://doi.org/10.1090/S0002-9939-1992-1077789-X

MathSciNet review:
1077789

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that each "component" of the polynomial convex hull of the support of the generating measure attracts zeros of the corresponding orthogonal polynomials. On the other hand, an example is given showing e.g. that mass points in the support need not attract zeros.

**[1]**G. Freud,*Orthogonal polynomials*, Akad. Kiadó, Budapest, 1971.**[2]**E. B. Saff,*Orthogonal polynomials from a complex perspective*, Orthogonal polynomials (Columbus, OH, 1989) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 294, Kluwer Acad. Publ., Dordrecht, 1990, pp. 363–393. MR**1100302**, https://doi.org/10.1007/978-94-009-0501-6_17**[3]**Herbert Stahl and Vilmos Totik,*General orthogonal polynomials*, Encyclopedia of Mathematics and its Applications, vol. 43, Cambridge University Press, Cambridge, 1992. MR**1163828****[4]**Herbert Stahl and Vilmos Totik,*𝑛th root asymptotic behavior of orthonormal polynomials*, Orthogonal polynomials (Columbus, OH, 1989) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 294, Kluwer Acad. Publ., Dordrecht, 1990, pp. 395–417. MR**1100303****[5]**Pál Turán,*On some open problems of approximation theory*, Mat. Lapok**25**(1974), no. 1–2, 21–75 (1977) (Hungarian). MR**0442540****[6]**Harold Widom,*Polynomials associated with measures in the complex plane*, J. Math. Mech.**16**(1967), 997–1013. MR**0209448**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
42C05,
30C99

Retrieve articles in all journals with MSC: 42C05, 30C99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1077789-X

Article copyright:
© Copyright 1992
American Mathematical Society