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 (*) 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 . Our results are a generalization of some earlier results due to J. Heittokangas and J. Gröhn.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-6,
author = {Li-Peng Xiao},
title = {Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {275-295},
zbl = {1336.34126},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-6}
}
Li-Peng Xiao. Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space. Annales Polonici Mathematici, Tome 113 (2015) pp. 275-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-6/