Geodesic
Estimates for polynomials in the unit disk with varying constant terms
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2.

Voir la notice de l'article provenant de la source Library of Science

Let · be the uniform norm in the unit disk. We study the quantities M_n(α) := inf(zP(z) + α-α) where the infimum is taken over all polynomials P of degree n-1 with P(z) = 1 and α gt; 0. In a recent paper by Fournier, Letac and Ruscheweyh (Math. Nachrichten 283 (2010), 193-199) it was shown that inf_α gt; 0 M_n(α) = 1/n. We find the exact values of M_n(α) and determine corresponding extremal polynomials. The method applied uses known cases of maximal ranges of polynomials.
Keywords: Bernstein-type inequalities for complex polynomials, maximal ranges for polynomials 
@article{AUM_2011_65_2_a4,
     author = {Ruscheweyh, Stephan and Wo{\l}oszkiewicz, Magdalena},
     title = {Estimates for polynomials in the unit disk with varying constant terms},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2011_65_2_a4/}
}
TY  - JOUR
AU  - Ruscheweyh, Stephan
AU  - Wołoszkiewicz, Magdalena
TI  - Estimates for polynomials in the unit disk with varying constant terms
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2011
VL  - 65
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2011_65_2_a4/
LA  - en
ID  - AUM_2011_65_2_a4
ER  - 
%0 Journal Article
%A Ruscheweyh, Stephan
%A Wołoszkiewicz, Magdalena
%T Estimates for polynomials in the unit disk with varying constant terms
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2011
%V 65
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2011_65_2_a4/
%G en
%F AUM_2011_65_2_a4
Ruscheweyh, Stephan; Wołoszkiewicz, Magdalena. Estimates for polynomials in the unit disk with varying constant terms. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2. http://geodesic.mathdoc.fr/item/AUM_2011_65_2_a4/

[1] Andrievskii, V., Ruscheweyh, S., Complex polynomials and maximal ranges: background and applications, Recent progress in inequalities (Nis, 1996), Math. Appl.,

[2] 430, Kluwer Acad. Publ., Dordrecht, 1998, 31-54.

[3] Córdova, A., Ruscheweyh, S., On maximal polynomial ranges in circular domains, Complex Variables Theory Appl. 10 (1988), 295-309.

[4] Córdova, A., Ruscheweyh, S., On maximal ranges of polynomial spaces in the unit disk, Constr. Approx. 5 (1989), 309-327.

[5] Fournier, R., Letac, G. and Ruscheweyh, S., Estimates for the uniform norm of complex polynomials in the unit disk, Math. Nachr. 283 (2010), 193-199.

[6] Ruscheweyh, S., Varga, R., On the minimum moduli of normalized polynomials with two prescribed values, Constr. Approx. 2 (1986), 349-368.