Abstract:
We find the necessary and sufficient conditions for the completeness and minimality in the space L2(0;1) of system (√xρkJν(xρk):k∈N) generated by Bessel function of the first kind of index ν⩾−1/2. Moreover, we establish a criterion for the completeness and minimality of system (x−2√xρkJ3/2(xρk):k∈N) in the space L2((0;1);x2dx).
\Bibitem{VinKha13}
\by B.~V.~Vynnyts'kyi, R.~V.~Khats'
\paper Completeness and minimality of systems of Bessel functions
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 2
\pages 131--141
\mathnet{http://mi.mathnet.ru/eng/ufa203}
\crossref{https://doi.org/10.13108/2013-5-2-131}
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\elib{https://elibrary.ru/item.asp?id=19063041}
Linking options:
https://www.mathnet.ru/eng/ufa203
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
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