HOLOMORPHIC APPROXIMATION AND MIXED BOUNDARY VALUE PROBLEMS FOR ∂

Christine Laurent-Thiébaut (1) , Mei-Chi Shaw (2)

1 IF - Institut Fourier
2 UND - University of Notre Dame [Indiana]

In this paper we study holomorphic approximation using boundary value problems for $\overline\partial$ on an annulus in the Hilbert space setting. The associated boundary conditions for $\overline\partial$ are the mixed boundary problems on an annulus. We characterize pseudoconvexity and Runge type property of the domain by the vanishing of related $L^2$ cohomology groups.

Mots clés: holomorphic approximation; Runge's theorem; Cauchy-Riemann operators

Domaines: Variables complexes [math.CV]

Christine Laurent-Thiébaut, Mei-Chi Shaw. HOLOMORPHIC APPROXIMATION AND MIXED BOUNDARY VALUE PROBLEMS FOR ∂. Proceedings of the American Mathematical Society, 2020, ⟨10.1090/proc/14979⟩. ⟨hal-02130127v2⟩