S. A. Telyakovskii, “Concerning a sufficient condition of Sidon for the integrability of trigonometric series”, Mat. Zametki, 14:3 (1973), 317–328; Math. Notes, 14:3 (1973), 742

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Matematicheskie Zametki, 1973, Volume 14, Issue 3, Pages 317–328 (Mi mzm7261)

This article is cited in 24 scientific papers (total in 24 papers)

Concerning a sufficient condition of Sidon for the integrability of trigonometric series

S. A. Telyakovskii

Steklov Mathematical Institute, Academy of Sciences of the USSR

Full-text PDF (625 kB) Citations (24)

Abstract: We consider problems concerning integrability and convergence in the metric

$L$ of trigonometric series, the coefficients

$a_k$ of which satisfy the conditions:

$a_k\to0$ , there exist numbers

$A_k$ such that

$A_k\downarrow0$ ,

$\sum A_k<\infty$ , and

$|\Delta a_k|\le A_k$ . The integrability of a series in cosines under these conditions is equivalent to a theorem of Sidon.

Received: 15.03.1973

English version:
Mathematical Notes, 1973, Volume 14, Issue 3, Pages 742–748
DOI: https://doi.org/10.1007/BF01147448

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: S. A. Telyakovskii, “Concerning a sufficient condition of Sidon for the integrability of trigonometric series”, Mat. Zametki, 14:3 (1973), 317–328; Math. Notes, 14:3 (1973), 742–748

Citation in format AMSBIB

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\paper Concerning a sufficient condition of Sidon for the integrability of trigonometric series

\jour Mat. Zametki

\yr 1973

\vol 14

\issue 3

\pages 317--328

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=328456}

\zmath{https://zbmath.org/?q=an:0281.42011}

\transl

\jour Math. Notes

\yr 1973

\vol 14

\issue 3

\pages 742--748

\crossref{https://doi.org/10.1007/BF01147448}

Linking options:

https://www.mathnet.ru/eng/mzm7261

https://www.mathnet.ru/eng/mzm/v14/i3/p317

This publication is cited in the following 24 articles:

N. Yu. Agafonova, S. S. Volosivets, “Integriruemost ryadov po multiplikativnym sistemam i obobschennye proizvodnye”, Izv. vuzov. Matem., 2024, no. 3, 3–14
N. Yu. Agafonova, S. S. Volosivets, “Integrability of Series with Respect to Multiplicative Systems and Generalized Derivatives”, Russ Math., 68:3 (2024), 1
Elijah Liflyand, Pathways in Mathematics, Harmonic Analysis on the Real Line, 2021, 23
Sandeep Kaur Chouhan, Jatinderdeep Kaur, Satvinder Singh Bhatia, “Extensions of Móricz Classes and Convergence of Trigonometric Sine Series in L1-Norm”, Mathematics, 6:12 (2018), 292
Peter K. Friz, Benjamin Gess, Archil Gulisashvili, Sebastian Riedel, “The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory”, Ann. Probab., 44:1 (2016)
Xhevat Z. Krasniqi, “Further results on $L^{1}$-convergence of some modified complex trigonometric sums”, J. Numer. Anal. Approx. Theory, 44:2 (2015), 180
Elijah Liflyand, “On Fourier Re-Expansions”, J Fourier Anal Appl, 20:5 (2014), 934
Kuznetsova O.I., “Strong Summability and Convergence of Multiple Trigonometric Series Over Polyhedrons”, J. Contemp. Math. Anal.-Armen. Aca., 47:5 (2012), 240–250
E. Liflyand, S. Samko, R. Trigub, “The Wiener algebra of absolutely convergent Fourier integrals: an overview”, Anal.Math.Phys., 2:1 (2012), 1
Zaderei, PV, “ON SIDON-TELYAKOVSKII-TYPE CONDITIONS FOR THE INTEGRABILITY OF MULTIPLE TRIGONOMETRIC SERIES”, Ukrainian Mathematical Journal, 60:5 (2008), 663
Tomovski Zivorad, “An extension of the Garrett-Stanojevic class”, Approx. Theory & its Appl., 16:1 (2000), 46
David E. Grow, Časlav V. Stanojević, “Convergence and the Fourier character of trigonometric transforms with slowly varying convergence moduli”, Math. Ann., 302:1 (1995), 433
Ferenc Móricz, “On the integrability and 𝐿¹-convergence of complex trigonometric series”, Proc. Amer. Math. Soc., 113:1 (1991), 53
Ferenc Móricz, Ferenc Schipp, “On the integrability and L1-convergence of Walsh series with coefficients of bounded variation”, Journal of Mathematical Analysis and Applications, 146:1 (1990), 99
Shu Yun Sheng, “The extension of the theorems of Č. V. Stanojević and V. B. Stanojević”, Proc. Amer. Math. Soc., 110:4 (1990), 895
Časlav V. Stanojević, “Structure of Fourier and Fourier-Stieltjes coefficients of series with slowly varying convergence moduli”, Bull. Amer. Math. Soc., 19:1 (1988), 283
Časlav V. Stanojević, Vera B. Stanojevic, “Generalizations of the Sidon-Telyakovskiǐ theorem”, Proc. Amer. Math. Soc., 101:4 (1987), 679
Vera B Stanojevic, “Convergence of Fourier series with complex quasimonotone coefficients and coefficients of bounded variation of order m”, Journal of Mathematical Analysis and Applications, 115:2 (1986), 482
G. A. Fomin, “On some classes of Jacobi orthogonal series”, Math. USSR-Sb., 55:1 (1986), 121–132
William O. Bray, Vera B. Stanojevic, “On the integrability of complex trigonometric series”, Proc. Amer. Math. Soc., 93:1 (1985), 51

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

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