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 Eurasian Math. J., 2015, Volume 6, Number 1, Pages 123–131 (Mi emj189)

On the completeness and minimality of sets of Bessel functions in weighted $L^2$-spaces

B. V. Vynnyts'kyi, R. V. Khats'

Institute of Physics, Mathematics, Economics and Innovation Technologies, Drohobych Ivan Franko State Pedagogical University, 3 Stryis'ka St., 82100 Drohobych, Ukraine

Abstract: We establish a criterion for the completeness and minimality of the system $(x^{-p-1}\sqrt{x\rho_k}J_\nu(x\rho_k):k\in\mathbb{N})$ in the space $L^2((0;1); x^{2p}dx)$ where $J_\nu$ is the Bessel function of the first kind of index $\nu\geqslant1/2$, $p\in\mathbb{R}$ and $(\rho_k : k\in\mathbb{N})$ is a sequence of distinct nonzero complex numbers.

Keywords and phrases: Bessel function, entire function, complete system, minimal system, biorthogonal system.

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MSC: Primary 30B60, 33C10, 34B30, 42A65; Secondary 30D10, 30D20, 44A15, 46E30
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Citation: 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

Citation in format AMSBIB
\Bibitem{VinKha15} \by B.~V.~Vynnyts'kyi, R.~V.~Khats' \paper On the completeness and minimality of sets of Bessel functions in~weighted $L^2$-spaces \jour Eurasian Math. J. \yr 2015 \vol 6 \issue 1 \pages 123--131 \mathnet{http://mi.mathnet.ru/emj189} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000374499100010} 

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This publication is cited in the following articles:
1. 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
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