arXiv subjects

Gilad Reti

Publications and source records attributed to Gilad Reti.

2 recordsLinked to original sources

arXiv2021

Crystalline temperate distributions with uniformly discrete support and spectrum

We prove that a temperate distribution on $\mathbb{R}$ whose support and spectrum are uniformly discrete sets, can be obtained from Poisson's summation formula by a finite number of basic operations (shifts, modulations, differentiations, multiplication by polynomials, and taking linear combinations).

math.CA↗

arXiv2020

Poisson summation formulas involving the sum-of-squares function

We obtain new Poisson type summation formulas with nodes $\pm \sqrt{n}$ and with weights involving the function $r_k(n)$ that gives the number of representations of a positive integer $n$ as the sum of $k$ squares. Our results extend summation formulas due to Guinand and Meyer that involve the sum-of-three-squares function $r_3(n)$.

math.CA↗