# Fourier Interpolation with Zeros of Zeta and L-Functions

@article{Bondarenko2022FourierIW, title={Fourier Interpolation with Zeros of Zeta and L-Functions}, author={Andriy V. Bondarenko and Danylo V. Radchenko and Kristian Seip}, journal={Constructive Approximation}, year={2022} }

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other L-functions. We establish a duality principle for Fourier interpolation bases in terms of certain kernels of general Dirichlet series with variable coefficients. Such kernels admit meromorphic continuation, with poles at a sequence dual to the sequence of frequencies of the Dirichlet…

## 2 Citations

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- MathematicsJournal of Fourier Analysis and Applications
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We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)bμ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

## References

SHOWING 1-10 OF 35 REFERENCES

### Fourier Interpolation and Time-Frequency Localization

- MathematicsJournal of Fourier Analysis and Applications
- 2021

We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)bμ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

### Hamburger’s Theorem on ζ(s) and the Abundance Principle for Dirichlet Series with Functional Equations

- Mathematics
- 2000

Ask any Ask any mathematician - indeed any number theorist - to state Hamburger’s theorem; chances are the response will be something like, “Riemann’s function ζ(s) is uniquely determined by its…

### Fourier interpolation on the real line

- MathematicsPublications mathématiques de l'IHÉS
- 2018

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the…

### On Dirichlet series satisfying Riemann's functional equation

- Mathematics
- 1994

SummaryAccording to convention, Hamburger's theorem (1921) says-roughly-that Riemann's ζ(s) is uniquely determined by its functional equation. In 1944 Hecke pointed out that there are two distinct…

### Some comments on Fourier analysis, uncertainty and modeling

- Mathematics
- 1983

Investigation of the problem of simultaneously concentrating a function . and its Fourier transform has led to some interesting special functions that have widespread applications in engineering.…

### The Eigenvalue Distribution of Time-Frequency Localization Operators

- Mathematics
- 2015

We estimate the distribution of the eigenvalues of a family of time-frequency localization operators whose eigenfunctions are the well-known Prolate Spheroidal Wave Functions from mathematical…

### Heisenberg uniqueness pairs and the Klein-Gordon equation

- Mathematics
- 2009

A Heisenberg uniqueness pair (HUP) is a pair ( , ), where is a curve in the plane and is a set in the plane, with the following property: any finite Borel measure µ in the plane supported on , which…