Turkish Journal of Mathematics
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 $(\rho_k)_{k\in\mathbb N}$.
DOI
10.3906/mat-2101-76
Keywords
Bessel function, entire function, complete system, minimal system, basis, weighted space
First Page
890
Last Page
895
Recommended Citation
KHATS', R (2021). Completeness conditions of systems of Bessel functions in weighted $L^2$-spaces in terms of entire functions. Turkish Journal of Mathematics 45 (2): 890-895. https://doi.org/10.3906/mat-2101-76
