Abstract
Using results of Part I of this paper, we shall now develop two methods of constructing linear partial differential equations which admit Bergman operators with polynomial kernels; these equations will be obtained explicitly. Those methods will also yield general representations of solutions of such an equation which are holomorphic in some domain of complex two-space. For generating all those solutions, one needs a pair of Bergman operators. Whereas in Part I of this paper we required at least one of the two operators to have a polynomial kernel, we now impose the condition that both operators be of that kind. This entails further basic results about the existence, construction, and uniqueness of solutions.
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Kracht, M., Kreyszig, E. Zur Konstruktion gewisser Integraloperatoren für partielle Differentialgleichungen Teil II. Manuscripta Math 17, 171–186 (1975). https://doi.org/10.1007/BF01154088
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DOI: https://doi.org/10.1007/BF01154088