**
Below is the ascii version of the abstract for 96-457.
The html version should be ready soon.**Neidhardt H., Zagrebnov V.A.
Does each symmetric operator have a stability domain ?
(58K, LateX)
ABSTRACT. We show that any symmetric operator has a dense maximal stability domain,
where it is semibounded from below,if and only if it is unbounded from above.
This result allows an application to singular perturbed Schrodinger operators
which are not semibounded from below,i.e.,to the so-called fall to the centre
problem.We give an example of singular perturbed Schrodinger operator for
which stability domains are described explicitly.