On fourier transform, parseval equality, and the inversion formula in idempotent analysis

In the paper we revisit some known remarkable formulas and their idempotent versions highlighting the role of functional spaces. More precisely, we focus on the space where the analogue of the Fourier transform takes place, the Legendre transform in ℝ
_min
and the concave conjugate transform in ℝ
_max
, then we give the analogues of some classical theorems.