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**Extra resources for Several Complex Variables V: Complex Analysis in Partial Differential Equations and Mathematical Physics **

**Example text**

6) (the choice of Q(z) is strictly related to the Noetherian operators which we have already described in Chap. 1). 6). 6). 6). 6) is replaced by with p E &‘(lR”), f E E(IRn): P * f(z) Recall that the definition := (Pt, t - of convolution is f(x - t)). A. C. Struppa by Palamodov (Palamodov [1970]). Th eir result, to which we will always refer by the name of Pandamental Principle (according to Ehrenpreis’s own terminology) is a much stronger generalization of Euler’s principle than the approximation theorem is.

6) is replaced by with p E &‘(lR”), f E E(IRn): P * f(z) Recall that the definition := (Pt, t - of convolution is f(x - t)). A. C. Struppa by Palamodov (Palamodov [1970]). Th eir result, to which we will always refer by the name of Pandamental Principle (according to Ehrenpreis’s own terminology) is a much stronger generalization of Euler’s principle than the approximation theorem is. 6), with only the use of integrals and sums of exponential polynomial solutions: To be precise, we shall state the Fundamental Principle for the case of a single partial differential operator acting on & = &(R”); but its proof (as we shall soon see) holds in a much wider situation.

John (John [1955]).