G. G. Gevorkyan, “Majorants and uniqueness of series in the Franklin system”, Mat. Zametki, 59:4 (1996), 521–545; Math. Notes, 59:4 (1996), 373

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Matematicheskie Zametki, 1996, Volume 59, Issue 4, Pages 521–545
DOI: https://doi.org/10.4213/mzm1747 (Mi mzm1747)

This article is cited in 12 scientific papers (total in 12 papers)

Majorants and uniqueness of series in the Franklin system

G. G. Gevorkyan

Yerevan State University

Full-text PDF (254 kB) Citations (12)

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DOI: https://doi.org/10.4213/mzm1747

Abstract: It is proved that if a series in the Franklin system converges almost everywhere to a function

$f(t)$ and the distribution function of the majorant of partial sums satisfies the condition

$\operatorname{mes}\bigl\{t\in[0,1]:s(t)>\lambda\bigr\} =o\biggl(\frac 1\lambda\biggr)$
as

$\lambda\to\infty$ , then this series is a Fourier series for Lebesgue integrable functions

$f(t)$ . In the general case the coefficients of the series are reconstructed by means of an

$A$ -integral.

Received: 05.01.1995

English version:
Mathematical Notes, 1996, Volume 59, Issue 4, Pages 373–391
DOI: https://doi.org/10.1007/BF02308686

Bibliographic databases:

UDC: 517.98

Language: Russian

Citation: G. G. Gevorkyan, “Majorants and uniqueness of series in the Franklin system”, Mat. Zametki, 59:4 (1996), 521–545; Math. Notes, 59:4 (1996), 373–391

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1747

https://doi.org/10.4213/mzm1747

https://www.mathnet.ru/eng/mzm/v59/i4/p521

This publication is cited in the following 12 articles:

K. A. Keryan, A. L. Khachatryan, “A uniqueness theorem for orthonormal spline series”, Acta Math. Hungar., 2024
G. G. Gevorkyan, K. A. Navasardyan, “On uniqueness of series by general Franklin system”, J. Contemp. Math. Anal., 53:4 (2018), 223–231
K. A. Navasardyan, “On a uniqueness theorem for the Franklin system”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:2 (2018), 93–100
G. G. Gevorkyan, “Uniqueness Theorem for Multiple Franklin Series”, Math. Notes, 101:2 (2017), 219–229
K. A. Navasardyan, “Uniqueness theorems for multiple Franklin series”, Uch. zapiski EGU, ser. Fizika i Matematika, 51:3 (2017), 241–249
Gevorkyan G.G. Poghosyan M.P., “On Recovery of Coefficients of Franklin Series With a “Good” Majorant of Partial Sums”, J. Contemp. Math. Anal.-Armen. Aca., 52:5 (2017), 254–260
G. G. Gevorkyan, K. A. Navasardyan, “On Haar series of $A$-integrable functions”, J. Contemp. Math. Anal., 52:3 (2017), 149–160
G. G. Gevorkyan, “Uniqueness Theorems for Series in the Franklin System”, Math. Notes, 98:5 (2015), 847–851
G. G. Gevorgyan, A. S. Martirosyan, “Majorant and Paley function for series in general Franklin systems”, Proc. Steklov Inst. Math., 280 (2013), 132–143
Keryan K.A., Martirosyan A.S., “A Uniqueness Theorem for Series by Stromberg's System”, J. Contemp. Math. Anal.-Armen. Aca., 47:6 (2012), 278–292
V. V. Kostin, “Generalization of the Balashov Theorem on Subseries of the Fourier–Haar Series”, Math. Notes, 76:5 (2004), 689–696
V. V. Kostin, “Reconstructing Coefficients of Series from Certain Orthogonal Systems of Functions”, Math. Notes, 73:5 (2003), 662–679

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

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