Glasnik Matematicki, Vol. 35, No.1 (2000), 111-136.

EVOLUTION EQUATIONS AS OPERATOR EQUATIONS IN LATTICES OF HILBERT SPACES

Rainer Picard

Abstract.   Evolution equations are considered as operator equations involving a sum of the time-derivative operator ∂₀ regarded as a normal operator in a suitable Hilbert space setting and another fairly arbitrary spatial operator A acting in a Hilbert space H. The initial data are then modeled as H-valued δ-type sources located at time 0. A framework to discuss this and more general types of evolution problems is constructed. The solution theory relies on a Fouries-Laplace transform method set in this framework.

1991 Mathematics Subject Classification.   47D06, 44A05.