Linear differential equations with solutions lying in weighted Fock spaces. Issue 2 (1st February 2021) - Hu, Guangming; Huusko, Juha-Matti; Long, Jianren; Sun, Yu
Abstract : Sufficient conditions for coefficients of the non-homogeneous linear complex differential equation f ( k ) + A k − 1 ( z ) f ( k − 1 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = A k ( z ) are found such that all solutions belong to some weighted Fock spaces, where A j ( z ) are entire functions, j = 0, 1, …, k . Furthermore, sufficient conditions for the coefficient A ( z ) such that all solutions of the special second order equation f ″ + A ( z ) f = 0 belong to some weighted Fock spaces are given by the Bergman reproducing kernel, where A ( z ) is an entire function.