On the singular continuous spectrum of self-adjoint extensions.
We give several conditions implying that the spectral bound of the generator of a -semigroup is negative. Applications to stability theory are considered.
We calculate the spectral multiplicity of the direct sum T⊕ A of a weighted shift operator T on a Banach space Y which is continuously embedded in and a suitable bounded linear operator A on a Banach space X.
We study the spectral properties of some group of unitary operators in the Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube (see formula (1)). Applying the Genchev transform ([2], [5]) we prove that this group has continuous simple spectrum (Theorem 4) and that the projection-valued measure for this group has a very explicit form (Theorem 5).