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.
Copyright © 2017 Springer. This article first appeared in Computational Methods and Function Theory 17:3 (2017), 499-523.
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Cheng, Raymond, Javad Mashreghi, and William T. Ross. "Birkhoff–James Orthogonality and the Zeros of an Analytic Function." Computational Methods and Function Theory 17, no. 3 (2017): 499-523. doi:10.1007/s40315-017-0191-5.