A Complete Classification of Fourier Summation Formulas on the real line

Felipe Gonçalves, Guilherme Vedana

We completely classify Fourier summation formulas of the form $${\int }_{\mathbb{R}}\hat{\phi }(t)d\mu (t)=\sum _{n=0}^{\infty }a({\lambda }_n)\phi ({\lambda }_n),$$ that hold for any test function $\phi$, wher…