Linear Differential Equations with Coefficients in Fock Type Space
نویسندگان
چکیده
where the coefficients are entire functions. In [8], equations of the form (1) with coefficients in weighted Bergman or Hardy spaces are studied. The direct problem is proved, that is, if the coefficients aj(z), j = 0, ..., k − 1 of (1) belong to the weighted Bergman space, then all solutions are of finite order of growth and belong to weighted Bergman space. The inverse problem is also investigated, that is, if all solutions are of finite order of growth, then the coefficient is proved to belong to weighted Bergman space. The Bargmann-Fock space (see [1], [2]) is the Hilbert space of entire functions equipped with the inner product
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