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Computational Methods and Function Theory 7 (2007), No. 2, 371--378
Copyright Heldermann Verlag 2007

An Extension of Jack's Lemma to Polynomials of Fixed Degree

Richard Fournier
fournier@dms.umontreal.ca , CRM and Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Québec, Canada.

Marius Serban
marius.serban@umontreal.ca , Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Québec, H3C 3J7, Canada.

[Abstract-pdf] [Abstract-ps]

We study an extension of Jack's lemma to polynomials of fixed degree. Our result is based on a class of bound-preserving operators over polynomials introduced by Ruscheweyh.

Keywords: Jack's lemma, bound-preserving operators, extremal polynomials.

MSC 2000: Primary 30C80; Secondary 30C10.

[FullText-pdf (232 K)] [FullText-ps (390 K)]