Virginia State University
Title: A Study of Bernstein Inequality for Self Reciprocal Polynomials of Degree Two and Related Subclasses
Director(s): Dawit Haile
Dates of Program: May 21 - June 30, 2007
Summary: Denote the class of all algebraic polynomials of degree at most n by Pn. It is well known from Bernstein's Theorem that . Equality holds if and only if p(z) = czn, c is a constant.
This inequality has been improved under several kinds of restrictions. Consider a subclass consisting of all polynomials which has the property p(z) = znp(1/z). The question is if , what is the best estimate of in terms of ?
Using basic results from Complex Analysis and knowledge of Trigonometry and Calculus, students will explore the case when n = 3. They will also give an alternative proof for the known case when n = 2.
Student Researchers Supported by MAA:
- Aaron Sturgis
- Andrea Sims
- Merlin Woodlin
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