The paper deals with initial value problems of the form
in where is a linear first order differential operator. The desired solutions will be sought in function spaces defined as kernel of a linear differential operator being associated to . Mainly two assumptions are required for such initial value problems to be solvable: Firstly, the operators have to be associated, i.e. implies . Secondly, an interior estimate (with ) must be true. Moreover, operators are investigated possessing a family of associated operators (which then are said to be co-associated).
The present paper surveys the use of associated and co-associated differential operators for solving initial value problems of the above (Cauchy-Kovalevskaya) type. Discussing interior estimates as starting point for the construction of related scales of Banach spaces, the paper sets up a possible framework for further generalizations. E.g., that way a theorem of Cauchy-Kovalevskaya type with initial functions satisfying a differential equation of an arbitrary order k (with not necessarily analytic coefficients) is obtained.
Cite this article
R. Heersink, Wolfgang Tutschke, On Associated and Co-Associated Complex Differential Operators. Z. Anal. Anwend. 14 (1995), no. 2, pp. 249–257DOI 10.4171/ZAA/674