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Transactions of the American Mathematical Society

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Decomposition theorems and approximation by a “floating" system of exponentials


Author: E. S. Belinskii
Journal: Trans. Amer. Math. Soc. 350 (1998), 43-53
MSC (1991): Primary 42A61
DOI: https://doi.org/10.1090/S0002-9947-98-01556-6
MathSciNet review: 1340169
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Abstract: The main problem considered in this paper is the approximation of a trigonometric polynomial by a trigonometric polynomial with a prescribed number of harmonics. The method proposed here gives an opportunity to consider approximation in different spaces, among them the space of continuous functions, the space of functions with uniformly convergent Fourier series, and the space of continuous analytic functions. Applications are given to approximation of the Sobolev classes by trigonometric polynomials with prescribed number of harmonics, and to the widths of the Sobolev classes. This work supplements investigations by Maiorov, Makovoz and the author where similar results were given in the integral metric.


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Additional Information

E. S. Belinskii
Affiliation: Department of Mathematics, Technion, 32000, Haifa, Israel
Address at time of publication: Department of Mathematics, University of Zimbabwe, P. O. Box MP167, Mount Pleasant, Harare, Zimbabwe
Email: belinsky@maths.uz.zw

Keywords: Approximation, width
Received by editor(s): March 13, 1995
Additional Notes: This research was supported by the Israeli Ministry of Science and the Arts through the Ma’agara program for absorption of immigrant mathematicians at the Technion, Israel Institute of Technology
Article copyright: © Copyright 1998 American Mathematical Society