Turkish Journal of Mathematics
DOI
10.3906/mat-2101-76
Abstract
Let $J_{\nu}$ be the Bessel function of the first kind of index $\nu\ge 1/2$, $p\in\mathbb R$ and $(\rho_k)_{k\in\mathbb N}$ be a sequence of distinct nonzero complex numbers. Sufficient conditions for the completeness of the system $\big\{x^{-p-1}\sqrt{x\rho_k}J_{\nu}(x\rho_k):k\in\mathbb N\big\}$ in the weighted space $L^2((0;1);x^{2p} dx)$ are found in terms of an entire function with the set of zeros coinciding with the sequence $(\rho_k)_{k\in\mathbb N}$.
Keywords
Bessel function, entire function, complete system, minimal system, basis, weighted space
First Page
890
Last Page
895
Recommended Citation
KHATS', RUSLAN
(2021)
"Completeness conditions of systems of Bessel functions in weighted $L^2$-spaces in terms of entire functions,"
Turkish Journal of Mathematics: Vol. 45:
No.
2, Article 17.
https://doi.org/10.3906/mat-2101-76
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss2/17
