On the Cauchy problem for the debar operator

TL;DR

This paper investigates the solvability of the Cauchy problem for the debar operator on weakly pseudoconvex hypersurfaces, providing new theoretical insights and illustrative examples.

Contribution

It offers novel results on the solvability conditions of the debar operator's Cauchy problem in complex analysis.

Findings

New solvability criteria for the debar operator

Counterexamples illustrating non-solvability cases

Enhanced understanding of boundary conditions in complex analysis

Abstract

We present new results concerning the solvability, of lack thereof, in the Cauchy problem for the debar operator, with initial values assigned on a weakly pseudoconvex hypersurface, and provide illustrative examples.