Propagation of Holomorphic Extendability of CR Functions.
This paper is an outgrowth of a paper by the first author on a generalized Hartogs Lemma. We complete the discussion of the nonlinear ∂̅ problem ∂f/∂z̅ = ψ(z,f(z)). We also simplify the proofs by a different choice of Banach spaces of functions.
We complete the characterization of singular sets of separately analytic functions. In the case of functions of two variables this was earlier done by J. Saint Raymond and J. Siciak.
This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables.The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
The authors obtain a generalization of Jack-Miller-Mocanu’s lemma and, using the technique of subordinations, deduce some properties of holomorphic mappings from the unit polydisc in into .
A Cauchy-Morera theorem is proved for a function of complex variables, assuming only . A related result of Bochner, concerning continuous functions, is extended to a larger function class.