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Birkhoff–James Orthogonality and the Zeros of an Analytic Function

Birkhoff–James Orthogonality and the Zeros of an Analytic Function 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 $$\ell ^p$$ ℓ p with $$p \in (1, \infty )$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Birkhoff–James Orthogonality and the Zeros of an Analytic Function

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References (31)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-017-0191-5
Publisher site
See Article on Publisher Site

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 $$\ell ^p$$ ℓ p with $$p \in (1, \infty )$$ 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.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 27, 2017

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