P. Tankam Laboratoire Hubert Curien (UMR 5516 CNRS), Université de Lyon, Université Jean-Monnet, 42000, Saint-Etienne, France T. Lépine [email protected] Laboratoire Hubert Curien (UMR 5516 CNRS), Université de Lyon, Université Jean-Monnet, 42000, Saint-Etienne, France Institut d’Optique Rhône-Alpes 18 rue Benoı̂t Lauras 42000, Saint-Etienne, France F. Castignoles Presbeasy, Lyon...

Let H be a separable infinite-dimensional Hubert space over R. The Fresnel class T(H) of H consists of all Fourier-Stieltjes transforms of bounded Borel measures on H. There are several results insuring that various functions of interest in connection with the Feynman integral and quantum mechanics are in 7{H). We give a theorem which has most of these results as corollaries as well as many fur...