On a Trace Functional for Formal Pseudo-Differential Operators and the Symplectic Structure of the Korteweg-Devries Type Equation.
We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.