Decomposition theorems and approximation by a “floating" system of exponentials
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- by E. S. Belinskii PDF
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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.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- 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