Abstract
Sufficient conditions for coefficients of the non-homogeneous linear complex differential equation are found such that all solutions belong to some weighted Fock spaces, where are entire functions, . Furthermore, sufficient conditions for the coefficient such that all solutions of the special second order equation belong to some weighted Fock spaces are given by the Bergman reproducing kernel, where is an entire function.
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Acknowledgments
We thank the referees for many important and useful comments. The first author would like to thank Department of Physics and Mathematics, University of Eastern Finland, for providing a good environment during the preparation of this work.
Disclosure statement
No potential conflict of interest was reported by the authors.