arXiv subjects

Gautam Bharali

Publications and source records attributed to Gautam Bharali.

38 records · Page 3Linked to original sources

arXiv2004

The role of Fourier modes in extension theorems of Hartogs-Chirka type

We generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of graph(F)\cup(\partial D\times D) -- where D is the open unit disc and graph(F) denotes the graph of a continuous D-valued function F -- to the bidisc. We extend holomorphic functions by applying the Kontinuitaetssatz to certain continuous families of analytic annuli, which is a procedure suited to configurations not covered by Chirka's theorem.

math.CV↗

arXiv2003

On peak-interpolation manifolds for A(Ω) for convex domains in C^n

Let Ωbe a bounded, weakly convex domain in C^n, n>1, having real-analytic boundary. A(Ω) is the algebra of all functions holomorphic in Ωand continuous upto the boundary. A submanifold M\subset \partialΩis said to be complex-tangential if T_p(M) lies in the maximal complex subspace of T_p(\partialΩ) for each p \in M. We show that for real-analytic submanifolds M\subset \partialΩ, if M is complex-tangential, then every compact subset of M is a peak-interpolation set for A(Ω).

math.CV↗