A note is made on the connection between Cliiord analysis and the Weyl functional calculus for an n-tuple of bounded selfadjoint operators which do not necessarily commute with each other.

It is shown that on every finite network with at least one circuit there exist second order differential operators having an infinite number of nonreal eigenvalues. The presence of nonreal eigenvalues implies that these operators cannot be selfadjoint with respect to any metric. These eigenvalues reveal also the existence of oscillatory solutions for the corresponding time–dependent partial dif...

A family of selfadjoint operators of the Friedrichs model is considered. These symmetric type operators have one singular point, zero of order m. For every m > 3/2, we construct a rank 1 perturbation from the class Lip1 such that the corresponding operator has a sequence of eigenvalues converging to zero. Thus, near the singular point, there is no singular spectrum finiteness condition in terms...

Krein space operator-theoretic methods are used to prove that the operator (sgnx)-j-j is similar to a selfadjoint operator in the Hubert space ¿2(R) • Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = Xwu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem in...