Multiplicative operators in the spaces of Schwartz families
Functional Analysis
2011-04-21 v1 Quantum Physics
Abstract
In this paper we introduce and study the multiplication among smooth functions and Schwartz families. This multiplication is fundamental in the formulation and development of a spectral theory for Schwartz linear operators in distribution spaces, to introduce efficiently the Schwartz eigenfamilies of such operators and to build up a good functional calculus for them. The definition of eigenfamily is absolutely natural and this new operation allows us to develop a rigorous and manageable spectral theory for Quantum Mechanics, since it appears in a form extremely similar to the current use in Physics.
Keywords
Cite
@article{arxiv.1104.3908,
title = {Multiplicative operators in the spaces of Schwartz families},
author = {David Carfí},
journal= {arXiv preprint arXiv:1104.3908},
year = {2011}
}