Harmonic representation of hyperfunctions defined on a hypersurface (Q2716168)

Let \(\Omega\) be a domain in \(\mathbb{R}^n\), \(n>1\), \(\rho\) be a real-analytic function, and \(\Gamma = \{z\in \Omega \mid \rho (z) = 0 \}\), \(d\rho \neq 0\) on \(\Gamma\), be a connected real-analytic relatively closed orientable hypersurface in \(\Omega\). NEWLINENEWLINENEWLINELet \(B\) be a bundle of hyperfunctions on \(\Gamma\). The authors derive a harmonic representation of the elements of \(B\), i.e., the representation of each hyperfunction of \(B\) as the difference of ``boundary'' values of two harmonic functions \(f^+\) and \(f^-\), whose domains are, respectively, \(\Omega ^+ = \{z\in \Omega \mid \rho (z) >0 \}\) and \(\Omega ^- = \{z\in \Omega \mid \rho (z) <0 \}\). NEWLINENEWLINENEWLINEThe authors extend the results and approach of \textit{L. Hörmander} [Linear partial differential operators (1976; Zbl 0321.35001)], of \textit{H. Komatsu} [Lect. Notes Math. 1495, 161-236 (1991; Zbl 0791.35003)], and of the first author and \textit{M. Sh. Yakimenko} [Sib. Math. Zh. 34, 113-122 (1993; Zbl 0817.32004)].NEWLINENEWLINEFor the entire collection see [Zbl 0959.00006].