Arithmetic and the Fuchs calculus

Abstract

Recall that, so as to protect ourselves from the large coefficient a₁(N) of δ₀ in $\mathfrak{T}_{N}^{1}$, we have dealt, most of the time, with functions w supported in [0, ∞[ or with a Fourier transform supported in the half-line. Now, there exists on the half-line a symbolic calculus of operators more suitable than the Weyl calculus, to wit the Fuchs calculus: its name stems from the way it adapts itself to the consideration of differential operators of Fuchs type on the half-line.