Carleman Approximation in One and Several Complex Variables

Harshith, Sairaj A (2023) Carleman Approximation in One and Several Complex Variables. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Harshith Sairaj A (Roll No. 18MS082)) Thesis_18MS082.pdf - Submitted Version Restricted to Repository staff only Download (863kB)

Abstract

In this project report, we study the Carleman approximation on the intersection of certain totally real sets. Carleman approximation has been studied on maximal totally real subspaces on Cn. It was shown by Manne, that the union of two maximal totally real subspaces on Cn that intersect only at the origin allows Carleman approximation when the union is polynomially convex. We will extend this result to the union of finitely many maximal totally real subspaces under certain criteria. Another class of Carleman sets are Lipschitz graphs. We show that the union of two Lipschitz graphs that meet only at the origin allows Carleman approximation if the union is polynomially convex. For this, we give a sufficient condition for the polynomial convexity of the union of two Lipschitz graphs.

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