Laguerre multiplier sequences and sector properties of entire functions
Matthew Chasse · Complex Variables and Elliptic Equations · 2011
We show that the class of multiplier sequences which can be interpolated by rational functions is the same as the class of multiplier sequences which can be interpolated by polynomials. In addition, a result of Obreschkoff is used to show that Jensen polynomials related to the Riemann ξ-function have only real zeros up to degree 1017. Partial results are stated concerning the problem of characterizing linear transformations which take polynomials whose zeros are constrained to lie in a sector to polynomials of the same type.