B. V. Vynnyts'kyi, R. V. Khats', “Completeness and minimality of systems of Bessel functions”, Ufa Math. J., 5:2 (2013), 131

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Ufa Mathematical Journal, 2013, Volume 5, Issue 2, Pages 131–141
DOI: https://doi.org/10.13108/2013-5-2-131 (Mi ufa203)

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

Completeness and minimality of systems of Bessel functions

B. V. Vynnyts'kyi, R. V. Khats'

Institute of Physics, Mathematics and Informatics, Ivan Franko Drohobych State Pedagogical University, 3 Stryiska Str., 82100 Drohobych, Ukraine

English version PDF (350 kB) Citations (9) Russian version article

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DOI: https://doi.org/10.13108/2013-5-2-131

Abstract: We find the necessary and sufficient conditions for the completeness and minimality in the space

$L^2(0;1)$ of system

$(\sqrt{x\rho_k}J_{\nu}(x\rho_k):k\in\Bbb N)$ generated by Bessel function of the first kind of index

$\nu\ge -1/2$ . Moreover, we establish a criterion for the completeness and minimality of system

$(x^{-2}\sqrt{x\rho_k}J_{3/2}(x\rho_k):k\in\Bbb N)$ in the space

$L^2((0;1);x^2 dx)$ .

Keywords: Paley–Wiener theorem, Bessel function, entire function, complete system, minimal system, biorthogonal system, basis.

Received: 30.01.2012

Bibliographic databases:

Document Type: Article

UDC: 517.5

MSC: 33C10, 30B60, 42A65, 42A38, 30D20, 42B10, 44A15, 30E15

Language: English

Original paper language: English

Citation: B. V. Vynnyts'kyi, R. V. Khats', “Completeness and minimality of systems of Bessel functions”, Ufa Math. J., 5:2 (2013), 131–141

Citation in format AMSBIB

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\paper Completeness and minimality of systems  of Bessel functions

\jour Ufa Math. J.

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\vol 5

\issue 2

\pages 131--141

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\crossref{https://doi.org/10.13108/2013-5-2-131}

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Linking options:

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https://doi.org/10.13108/2013-5-2-131

https://www.mathnet.ru/eng/ufa/v5/i2/p132

This publication is cited in the following 9 articles:

Ruslan Khats', “On the completeness of a system of Bessel functions of index -3/2 in weighted l2-space”, Filomat, 37:19 (2023), 6335
R. V. Khats', “Completeness of the System of Generalized Eigenfunctions for a Bessel-Type Differential Operator”, J Math Sci, 274:6 (2023), 898
Ruslan KHATS', “Generalized eigenvectors of linear operators and biorthogonal systems”, Constructive Mathematical Analysis, 5:2 (2022), 60
Ruslan Khats', “Integral representation of one class of entire functions”, Armen.J.Math., 14:1 (2022), 1
Khats V R., “On Conditions of the Completeness of Some Systems of Bessel Functions in the Space l-2((0; 1); X(2P)Dx)”, Azerbaijan J. Math., 11:1 (2021), 3–10
Khats R., “Completeness Conditions of Systems of Bessel Functions in Weighted l-2-Spaces in Terms of Entire Functions”, Turk. J. Math., 45:2 (2021), 890–895
B. V. Vynnyts'kyi, R. V. Khats', I. B. Sheparovich, “Unconditional bases of systems of Bessel functions”, Eurasian Math. J., 11:4 (2020), 76–86
B. V. Vynnyts'kyi, R. V. Khats', “On the completeness and minimality of sets of Bessel functions in weighted $L^2$-spaces”, Eurasian Math. J., 6:1 (2015), 123–131
Vynnyts'kyi B.V., Khats' R. V., “A Remark on Basis Property of Systems of Bessel and Mittag-Leffler Type Functions”, J. Contemp. Math. Anal.-Armen. Aca., 50:6 (2015), 300–305

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

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Abstract page:	1071
Russian version PDF:	167
English version PDF:	40
References:	126
First page:	2

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