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 Submission Date: October 22, 2018 Revision Date: January 18, 2019 Accteptance Date: January 25, 2019

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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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Keywords

• Best approximation
• Hardy space
• non-negative trigonometric polynomials

MSC

•  30C45
•  30C50

References

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