DOI

10.1007/s40315-017-0191-5

Abstract

Bounds are obtained for the zeros of an analytic function on a disk in terms of the Taylor coefficients of the function. These results are derived using the notion of Birkhoff–James orthogonality in the sequence space ℓp with p ∈ (1,∞), along with an associated Pythagorean theorem. It is shown that these methods are able to reproduce, and in some cases sharpen, some classical bounds for the roots of a polynomial.

Document Type

Article

Publication Date

2017

Publisher Statement

Copyright © 2017 Springer. This article first appeared in Computational Methods and Function Theory 17:3 (2017), 499-523.

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