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Eurasian Mathematical Journal, 2015, Volume 6, Number 1, Pages 123–131
(Mi emj189)
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This article is cited in 3 scientific papers (total in 3 papers)
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.
Received: 02.07.2014
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
Linking options:
https://www.mathnet.ru/eng/emj189 https://www.mathnet.ru/eng/emj/v6/i1/p123
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Abstract page: | 624 | Full-text PDF : | 112 | References: | 68 |
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