A boundary value problem with a discontinuous coefficient and containing a spectral parameter in the boundary condition.
Let be a -algebra, a compact abelian group, an action of by -automorphisms of the fixed point algebra of and the dense sub-algebra of -finite elements in . Further let be a linear operator from into which commutes with and vanishes on . We prove that is a complete dissipation if and only if is closable and its closure generates a -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite...
The existence of classical solutions for some partial differential equations on tori is shown.
A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.