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

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 115.3 (2015): 275-295. <http://eudml.org/doc/286074>.

@article{Li2015,
abstract = {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 $f^\{(k)\} + A_\{k-1\}f^\{(k-1)\} + ⋯ + A₁f^\{\prime \} + A₀f = 0$ (*) 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 . Our results are a generalization of some earlier results due to J. Heittokangas and J. Gröhn.},
author = {Li-Peng Xiao},
journal = {Annales Polonici Mathematici},
keywords = {Blaschke-oscillatory; Blaschke product; uniformly -separated sequence; Dirichlet space; prescribed zero sequence; differential equation},
language = {eng},
number = {3},
pages = {275-295},
title = {Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space},
url = {http://eudml.org/doc/286074},
volume = {115},
year = {2015},
}

TY - JOUR
AU - Li-Peng Xiao
TI - Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space
JO - Annales Polonici Mathematici
PY - 2015
VL - 115
IS - 3
SP - 275
EP - 295
AB - 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 $f^{(k)} + A_{k-1}f^{(k-1)} + ⋯ + A₁f^{\prime } + A₀f = 0$ (*) 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 . Our results are a generalization of some earlier results due to J. Heittokangas and J. Gröhn.
LA - eng
KW - Blaschke-oscillatory; Blaschke product; uniformly -separated sequence; Dirichlet space; prescribed zero sequence; differential equation
UR - http://eudml.org/doc/286074
ER -