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Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space

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Xiao L.-P.

Annales Polonici Mathematici

2015

tom 115

nr 3

275-295

The aim of this paper is to consider the following three problems:i (1) for a given uniformly q-separated sequence satisfying certain conditions, find a coefficient function A(z) analytic in the unit disc such that f''' + A(z)f = 0 possesses a solution having zeros precisely at the points of this sequence; (2) find necessary and sufficient conditions for the differential equation $f^{(k)} + A_{k-1}f^{(k-1)} + ⋯ + A₁f' + A₀f = 0$ (*) in the unit disc to be Blaschke-oscillatory; (3) find sufficient conditions on the analytic coefficients of the differential equation (*) for all analytic solutions to belong to the Dirichlet space 𝓓. Our results are a generalization of some earlier results due to J. Heittokangas and J. Gröhn.

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1 Annales Polonici Mathematici

1 Xiao L.-P.

1 2015

Wyniki wyszukiwania

Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space