On a class of unconditional bases in the weighted spaces of the entire functions whose order of growth is equal to 1/2 and on their applications (Q2777860)

The authors consider the Hilbert space \(A_\sigma^2(w^{-2})\) consisting of entire functions \(F\) of the order of growth 1/2 and the normal type that are square integrable with respect to a weight function \(w^{-2}\) (where \(w^2\) is a Muckenhoupt \(A_2\)-weight on \(\mathbb R_+\)) and such that \(h_F(-\pi)\leq \sigma\), where NEWLINE\[NEWLINE h_F(\alpha)=\limsup_{r\to \infty}r^{-1/2}\log |F(re^{i\alpha })|. NEWLINE\]NEWLINE A class of unconditional bases for the space \(A_\sigma^2(w^{-2})\) is constructed and applied to the problem of interpolation by entire functions. Isomorphic images of such bases in the space \(L_2(0,\sigma)\) are applied to investigation of the Sturm-Liouville operators with non-classical boundary conditions.