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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
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
Citation:
B. V. Vynnyts'kyi, R. V. Khats', “Completeness and minimality of systems of Bessel functions”, Ufa Math. J., 5:2 (2013), 131–141
Linking options:
https://www.mathnet.ru/eng/ufa203https://doi.org/10.13108/2013-5-2-131 https://www.mathnet.ru/eng/ufa/v5/i2/p132
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