RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 6, Pages 1393–1407 (Mi izv2018)

An estimate of the rate of approximation of a continuous function and its conjugate by Fourier sums on a set of total measure

K. I. Oskolkov

Abstract: In this paper, estimates of the rate of convergence almost everywhere of the Fourier series of a continuous function and its conjugate are obtained. These estimates, expressed in terms of its best approximation functions and its modulus of continuity, cannot be strengthened in a number of cases.

Full text: PDF file (1087 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1974, 8:6, 1372–1386

Bibliographic databases:

UDC: 517.512
MSC: Primary 41A25, 42A08, 42A20; Secondary 41A50

Citation: K. I. Oskolkov, “An estimate of the rate of approximation of a continuous function and its conjugate by Fourier sums on a set of total measure”, Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974), 1393–1407; Math. USSR-Izv., 8:6 (1974), 1372–1386

Citation in format AMSBIB
\Bibitem{Osk74} \by K.~I.~Oskolkov \paper An estimate of the rate of approximation of a~continuous function and its conjugate by Fourier sums on a~set of total measure \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1974 \vol 38 \issue 6 \pages 1393--1407 \mathnet{http://mi.mathnet.ru/izv2018} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=358198} \zmath{https://zbmath.org/?q=an:0307.42002} \transl \jour Math. USSR-Izv. \yr 1974 \vol 8 \issue 6 \pages 1372--1386 \crossref{https://doi.org/10.1070/IM1974v008n06ABEH002152} 

• http://mi.mathnet.ru/eng/izv2018
• http://mi.mathnet.ru/eng/izv/v38/i6/p1393

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. K. I. Oskolkov, “Approximation properties of summable functions on sets of full measure”, Math. USSR-Sb., 32:4 (1977), 489–514
2. V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117
3. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171
4. N Kirchhoff, R.J Nessel, “Divergence almost everywhere of a pointwise comparison of trigonometric convolution processes with their discrete analogues”, Journal of Approximation Theory, 70:1 (1992), 29
5. A. N. Bakhvalov, “Divergence everywhere of the Fourier series of continuous functions of several variables”, Sb. Math., 188:8 (1997), 1153–1170
6. A. N. Bakhvalov, “$\lambda$-Divergence of the Fourier Series of Continuous Functions of Several Variables”, Math. Notes, 72:4 (2002), 454–465
7. I. L. Bloshanskii, T. A. Matseevich, “A Weak Generalize Localization of Multiple Fourier Series of Continuous Functions with a Certain Module of Continuity”, Journal of Mathematical Sciences, 155:1 (2008), 31–46
8. St. Petersburg Math. J., 26:5 (2015), 741–756
9. D. A. Grafov, “Equiconvergence of expansions into triple trigonometric series and Fourier integral for continuous functions with a certain modulus of continuity”, Moscow University Mathematics Bulletin, 70:1 (2015), 24–32
•  Number of views: This page: 304 Full text: 109 References: 38 First page: 2