Traces of certain integral operators related to the riemann hypothesis

Sotelo-Pejerrey A. · AIMS Mathematics (2023) · DOI: 10.3934/math.20231274

Resumen

We prove the existence of a nontrivial singular trace τ defined on an ideal J closed with respect to the logarithmic submajorization such that τ(Aρ(α)) = 0, where Aρ(α): L2(0,1) → L2(0,1), [Aρ(α)f](θ) = ∫0 1 ρ(αθ/x)f (x)dx,0 < a ≤ 1. We also show that τ(Aρ(α)) = 0 for every τ nontrivial singular trace on J. Finally, we give a recursion formula from which we can evaluate all the traces Tr (Ar ρ(α)), r ∈ ℕ, r ≥ 2.

Instituciones: Universidad Continental