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Representation Formulas for the Class of Typically Real Polynomials

โœ Scribed by M. Brandt

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
285 KB
Volume
144
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Let Qn denote the class of polynomials of degree less than or equal to n that are univalent in the unit disk D and which are of the form (1) with real coefficients. The class Qn is a subclass of T,, of polynomials of degree les8 than or equal to n normalized by (1) which are real if and only if z is real, zE D, i.e. of the class of typically real polynom,ials. In this paper, formulas for the representation of the class Tn are derived. The application of these formulas t o appropriate extremal problems in Tn yields sharp estimates for the classes Tn and Qn. f ( z ) = z + a222 + ...

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