Flatness of conjugate reciprocal unimodular polynomials
نویسندگان
چکیده
منابع مشابه
Flatness of Conjugate Reciprocal Unimodular Polynomials
A polynomial is called unimodular if each of its coefficients is a complex number of modulus 1. A polynomial P of the form P (z) = ∑n j=0 ajz j is called conjugate reciprocal if an−j = aj , aj ∈ C for each j = 0, 1, . . . , n. Let ∂D be the unit circle of the complex plane. We prove that there is an absolute constant ε > 0 such that max z∈∂D |f(z)| ≥ (1 + ε) √ 4/3m , for every conjugate recipro...
متن کاملHow Far Is an Ultraflat Sequence of Unimodular Polynomials from Being Conjugate-reciprocal?
In this paper we study ultraflat sequences (Pn) of unimodular polynomials Pn ∈ Kn in general, not necessarily those produced by Kahane in his paper [Ka]. We examine how far is a sequence (Pn) of unimodular polynomials Pn ∈ Kn from being conjugate reciprocal. Our main results include the following. Theorem. Given a sequence (εn) of positive numbers tending to 0, assume that (Pn) is a (εn)-ultraf...
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متن کاملOn the Derivatives of Unimodular Polynomials
Let D be the open unit disk of the complex plane; its boundary, the unit circle of the complex plane, is denoted by ∂D. Let Pc n denote the set of all algebraic polynomials of degree at most n with complex coefficients. For λ ≥ 0, let K n def = {
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.06.020