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Birkhoff–James Orthogonality and the Zeros of an Analytic Function

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

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA

    Raymond Cheng

  2. Département de mathématiques et de statistique, Université Laval, Québec, QC, G1V 0A6, Canada

    Javad Mashreghi

  3. Department of Mathematics and Computer Science, University of Richmond, Richmond, VA, 23173, USA

    William T. Ross

Authors
  1. Raymond Cheng
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  2. Javad Mashreghi
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  3. William T. Ross
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Correspondence to William T. Ross.

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Communicated by Laurent Baratchart.

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Cheng, R., Mashreghi, J. & Ross, W.T. Birkhoff–James Orthogonality and the Zeros of an Analytic Function. Comput. Methods Funct. Theory 17, 499–523 (2017). https://doi.org/10.1007/s40315-017-0191-5

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  • DOI: https://doi.org/10.1007/s40315-017-0191-5

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