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

### EVOLUTION EQUATIONS AS OPERATOR EQUATIONS IN
LATTICES OF HILBERT SPACES

### Rainer Picard

Technische Universitat Dresden, FR Mathematik, Institut fur
Analysis, D-01062 Dresden, Germany

*e-mail:* `picard@math.tu-dresden.de`

**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.

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