A. A. Shkalikov, “A system of functions”, Mat. Zametki, 18:6 (1975), 855–860; Math. Notes, 18:6 (1975), 1097

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Matematicheskie Zametki, 1975, Volume 18, Issue 6, Pages 855–860 (Mi mzm7711)

This article is cited in 9 scientific papers (total in 9 papers)

A system of functions

A. A. Shkalikov

M. V. Lomonosov Moscow State University

Full-text PDF (455 kB) Citations (9)

Abstract: A system of functions

f_{k} (x) = \sum_{i = 1}^{r} α_{i} φ_{i} (x)^{k} + b_{i} {\bar{φ}}_{i} (x)^{k}, k = 1, 2, \dots

$f_k(x)=\sum_{i=1}^r\alpha_i\varphi_i(x)^k+b_i\overline\varphi_i(x)^k,\quad k=1,2,\dots$
is considered on the interval

[0, l]

$[0,l]$ .
Under certain conditions on the

φ_{i} (x)

$\varphi_i(x)$ , it is proved that the system

1 \cup {f_{k} (x)}_{k = 1}^{\infty}

$1\cup\{f_k(x)\}_{k=1}^\infty$ is complete in the space

L_{p} (0, l)

$L_p(0,l)$ . In the case

r = 1

$r=1$ it is proved, under certain additional assumptions, that the system

{f_{k} (x)}_{k = 0}^{\infty}

$\{f_k(x)\}_{k=0}^\infty$ is minimal.

Received: 20.01.1974

English version:
Mathematical Notes, 1975, Volume 18, Issue 6, Pages 1097–1100
DOI: https://doi.org/10.1007/BF01099988

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: A. A. Shkalikov, “A system of functions”, Mat. Zametki, 18:6 (1975), 855–860; Math. Notes, 18:6 (1975), 1097–1100

Citation in format AMSBIB

\Bibitem{Shk75}

\by A.~A.~Shkalikov

\paper A~system of functions

\jour Mat. Zametki

\yr 1975

\vol 18

\issue 6

\pages 855--860

\mathnet{http://mi.mathnet.ru/mzm7711}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=417683}

\zmath{https://zbmath.org/?q=an:0321.42013}

\transl

\jour Math. Notes

\yr 1975

\vol 18

\issue 6

\pages 1097--1100

\crossref{https://doi.org/10.1007/BF01099988}

Linking options:

https://www.mathnet.ru/eng/mzm7711

https://www.mathnet.ru/eng/mzm/v18/i6/p855

This publication is cited in the following 9 articles:

M. I. Ismailov, “On the Solvability of Riemann Problems in Grand Hardy Classes”, Math. Notes, 108:4 (2020), 523–537
B. T. Bilalov, “The basis property of a perturbed system of exponentials in Morrey-type spaces”, Siberian Math. J., 60:2 (2019), 249–271
B. T. Bilalov, F. A. Guliyeva, “A completeness criterion for a double power system with degenerate coefficients”, Siberian Math. J., 54:3 (2013), 419–424
B. T. Bilalov, “On solution of the Kostyuchenko problem”, Siberian Math. J., 53:3 (2012), 404–418
B. T. Bilalov, “The basis properties of power systems in $L_p$ ”, Siberian Math. J., 47:1 (2006), 18–27
A. A. Shkalikov, “Strongly damped pencils of operators and solvability of the corresponding operator-differential equations”, Math. USSR-Sb., 63:1 (1989), 97–119
Yu. I. Lyubarskii, “On the completeness and minimality of Rayleigh systems”, Russian Math. Surveys, 41:4 (1986), 179–180
Yu. I. Lyubarskii, V. A. Tkachenko, “System $\{e^{\alpha nz}\sin nz\}_1^\infty$ ”, Funct. Anal. Appl., 18:2 (1984), 144–146
A. G. Tumarkin, “Completeness of certain systems of functions”, Funct. Anal. Appl., 14:2 (1980), 150–151

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

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