## Abstract

Consider the class of exponential polynomials of the form f(z)=∑n=0N(∑k=0mncn,kzk)ehnz,0=h0<h1<h2<⋯<hN,such that the coefficients c_{n}_{,}_{k} are complex numbers with cn,mn≠0 for all n∈ { 0 , 1 , … , N}. Let Λf={λn,μn}n∈Z be the zero set of f, where {λn,μn}n∈Z:={…,λ-1,…,λ-1⏟μ-1-times,λ0,…,λ0⏟μ0-times,λ1,…,λ1⏟μ1-times,…}.We show that the upper Beurling uniform density of Λ _{f} is equal to h_{N}/ (2 π). Then based on results by Avdonin and Moran, we prove that if Λ _{f} is of neutral type, then there is a family of functions of generalized divided differences, denoted by E(Λ) , belonging to the span of the exponential system EΛ={tkeλnt:n∈Z,k=0,1,…,μn-1}, such that E(Λ) is a Riesz sequence in L^{2}(0 , T) for any T> h_{N}. If Λ _{f} is not of neutral type, we show that there exist real numbers u_{n} satisfying | Re (λ_{n}+ u_{n}) | = O(1) , so that the exponential system {tke(λn+un)t:n∈Z,k=0,1,…,μn-1}is a Riesz sequence in L^{2}(0 , T) for any T> h_{N}.

Original language | British English |
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Pages (from-to) | 307-319 |

Number of pages | 13 |

Journal | Archiv der Mathematik |

Volume | 120 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2023 |

## Keywords

- Beurling densities
- Divided differences
- Exponential polynomials
- Neutral type
- Riesz sequences

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