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

摘要

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 ℝmin and the concave conjugate transform in ℝmax, then we give the analogues of some classical theorems.