On the Completeness and Minimality of Sets of Bessel Functions in Weighted \( L^2 \)-Spaces - Vynnyts’kyi, Bohdan V.; Khats’, Ruslan V. (Eurasian Mathematical Journal, 2015)
We establish a criterion for the completeness and minimality of the system \( (x^{-p-1}\sqrt{ρ_k}J_ u(xρ_k) : k \in \mathbb{N}) \) in the space \( L^2((0,1); x^{2p}dx) \), where \( J_ u \) is the Bessel function of the first kind of index \( u ≥ 1/2 \), \( p \in \mathbb{R} \) and \( (ρ_k : k \in \mathbb{N}) \) is a sequence of distinct nonzero complex numbers.