A propos de “wedges” et d’“edges,” et de prolongements holomorphes. (On “wedges” and “edges” and holomorphic continuation). (French) Zbl 0629.32009

The author obtains the following results for functions defined in wedges with non linear edge: (I) If a function \(f_ 0\), continuous on an edge \(E\subset {\mathbb{C}}^{n+1}\) of real dimension \(2n+1\) and of class \({\mathcal C}^{k+2}\) (k\(\geq 0)\) has a continuation in the sense of the distribution to a holomorphic function f in a wedge with edge E [cf. M. S. Baouendi, C. H. Chang and F. Treves, J. Differ Geom. 18, 331-391 (1983; Zbl 0575.32019)], then \(f_ 0\) has f as continuous and then holomorphic continuation in any “strictly thinner” wedge, and (II) The “edge of the wedge theorem” for an edge of class \({\mathcal C}^ 1\), which is a totally real n-dimensional manifold of \({\mathbb{C}}^ n\). In the corresponding proofs of E. Bedford [Math. Ann. 230, 213-225 (1977; Zbl 0346.23020)] and S. I. Pinchuk [Math. USSR, Sbornik 23 (1974), 441-455 (1975; translation from Mat. Sbornik, n. Ser. 94(136), 468-482 (1974; Zbl 0307.32013)], the edge is supposed to be of class \({\mathcal C}^ 2\).
Reviewer: P.Caraman


32D15 Continuation of analytic objects in several complex variables
32A40 Boundary behavior of holomorphic functions of several complex variables
Full Text: DOI