Infinite dimensional parametric distributions

Abstract

Appropriate definitions and properties are introduced for the scale of Fréchet spaces, TP^B, and its corresponding dual space defined to be the class of infinite dimensional tempered distributions. A generalization of differentiation is introduced on the class of infinite dimensional tempered distributions. When the real time parameter is introduced into the setting, a new class of infinite parametric distributions are studied as solutions to generalized Schrödinger equations. The class of infinite dimensional exmpered distributions has different representations. It is within the context of their kernel representation that standard creation and annihilation operators are studied. All of these spaces are considered as generalizations of Fock spaces.

AMS (MOS):

• 46,81