  The purpose of this paper is to prove an interpolation formula involving
derivatives for entire functions of exponential type. We extend the
interpolation formula derived by J. Vaaler in [37, Theorem 9] to general $L^p$
de Branges spaces. We extensively use techniques from de Branges' theory of
Hilbert spaces of entire functions as developed in [6], but a crucial passage
involves the Hilbert-type inequalities as derived in [15]. We give applications
to homogeneous spaces of entire functions that involve Bessel functions and we
prove a uniqueness result for extremal one-sided band-limited approximations of
radial functions in Euclidean spaces.
