On the zero-free polynomial approximation problem

DOI10.1016/j.jat.2015.10.003zbMath1342.41007arXiv1501.00247OpenAlexW2137573198MaRDI QIDQ259092

Arthur A. Danielyan

Publication date: 10 March 2016

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00247

zbMATH Keywords

polynomial approximationcomplex-valued analytic functions

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Approximation with constraints (41A29) Approximation by polynomials (41A10) Capacity and harmonic measure in the complex plane (30C85) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (2)

Uniform approximation in the spherical distance by functions meromorphic on Riemann surfaces ⋮ Simultaneous zero-free approximation and universal optimal polynomial approximants

Cites Work

• Mergelyan's theorem for zero free functions
• Approximating functions by the Riemann zeta-function and by polynomials with zero constraints
• Approximation of and by the Riemann zeta-function
• Mergelyan's approximation theorem with nonvanishing polynomials and universality of zeta-functions
• Zero-free polynomial approximation on a chain of Jordan domains
• Mergelyan’s theorem with polynomials non-vanishing on unions of sets
• Mergelyan's Theorem on Uniform Polynomial Approximation.
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