Comparison of the best approximation of holomorphic functions from Hardy space

Volume 12, Issue 7, pp 412--419 http://dx.doi.org/10.22436/jnsa.012.07.01 Publication Date: March 08, 2019       Article History

Authors

F. G. Abdullayev - Mersin University, Mersin, Turkey. - Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan. V. V. Savchuk - Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine. D. Simsek - Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan.


Abstract

We compare the best approximations of holomorphic functions in the Hardy space \(H^1\) by algebraic polynomials and trigonometric polynomials. Particulary, we establish a class of functions \(f\in H^1\) for which the best trigonometric approximation do not coincide with the best algebraic approximation.


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