B. S. Kashin, S. I. Sharek, “Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series”, Mat. Zametki, 58:2 (1995), 218–230; Math. Notes, 58:2 (1995), 824

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Matematicheskie Zametki, 1995, Volume 58, Issue 2, Pages 218–230 (Mi mzm2038)

This article is cited in 2 scientific papers (total in 2 papers)

Logarithmic growth of the

$L^1$ -norm of the majorant of partial sums of an orthogonal series

B. S. Kashin^a, S. I. Sharek^b

^a Steklov Mathematical Institute, Russian Academy of Sciences
^b Case Western Reserve University

Full-text PDF (951 kB) Citations (2)

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Abstract: It is proved that for any

$N\times N$ orthogonal matrix

$A=\{a_{ij}\}$ we have

$\sum_{i=1}^N\max_{1\le n\le N}\biggl|\sum_{j=1}^na_{ij}\biggr| \ge\frac 1{30}N^{1/2}\log N.$
A multidimensional analog of this result is also established.

Received: 27.01.1995

English version:
Mathematical Notes, 1995, Volume 58, Issue 2, Pages 824–832
DOI: https://doi.org/10.1007/BF02304104

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: B. S. Kashin, S. I. Sharek, “Logarithmic growth of the

$L^1$ -norm of the majorant of partial sums of an orthogonal series”, Mat. Zametki, 58:2 (1995), 218–230; Math. Notes, 58:2 (1995), 824–832

Citation in format AMSBIB

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\by B.~S.~Kashin, S.~I.~Sharek

\paper Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series

\jour Mat. Zametki

\yr 1995

\vol 58

\issue 2

\pages 218--230

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1367220}

\zmath{https://zbmath.org/?q=an:0857.42019}

\transl

\jour Math. Notes

\yr 1995

\vol 58

\issue 2

\pages 824--832

\crossref{https://doi.org/10.1007/BF02304104}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TV39900019}

Linking options:

https://www.mathnet.ru/eng/mzm2038

https://www.mathnet.ru/eng/mzm/v58/i2/p218

This publication is cited in the following 2 articles:

V. V. Pernai, “Spaces Generated by the Generalized Majorant of Partial Sums”, Math. Notes, 96:1 (2014), 154–157
B. S. Kashin, “On the possibility of generalizing “correction” theorems”, Math. Notes, 62:6 (1997), 784–786

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

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Full-text PDF :	160
References:	70
First page:	3

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