Below is the ascii version of the abstract for 06-268. The html version should be ready soon.

Asao Arai
Heisenberg Operators, Invariant Domains and Heisenberg Equations of Motion
(65K, Latex2.09)

ABSTRACT.  An abstract operator theory is developed
on operators of the form
$A_H(t):=e^{itH}Ae^{-itH}, \, t\in \R$, with
$H$ a self-adjoint operator and $A$ a
linear operator on a Hilbert space (in the context of quantum mechanics,
$A_H(t)$ is called the Heisenberg
operator of $A$ with respect to $H$).
The following aspects are discussed:
(i) integral equations for $A_H(t)$ for a general class of $A$ ;
(ii) a sufficient condition for $D(A)$, the domain of $A$, to be left invariant
by $e^{-itH}$ for all $t \in \R$ ;
(iii) a mathematically rigorous formulation of the Heisenberg equation of motion
in quantum mechanics and
the uniqueness of its solutions ; (iv) invariant domains in the case where $H$ is
an abstract version
of Schr\"odinger and Dirac operators ; (v) applications to Schr\"odinger
operators with matrix-valued potentials and Dirac operators.