Surjective partial differential operators on real analytic functions defined on a halfspace


Let P(D) be a partial differential operator with constant coefficients and let A(ω) denote the real analytic functions defined on an open set ω ⊂ R<sup>n</sup>. Let H be an open halfspace. We show that P(D) is surjective on A(H) if and only if P(D) is surjective on A(R<sup>n</sup>) and P(D) has a hyperfunction elementary solution which is real analytic on H.

DOI Code: 10.1285/i15900932v25n2p39

Keywords: Partial differential equations; Elementary solutions; Surjectivity on real analytic functions

Classification: 35E20; 35E05; 35A20; 46F15

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