# A function algebra providing new Mergelyan type theorems in several complex variables

## TL;DR

This paper introduces a new function algebra for compact sets in several complex variables, enabling Mergelyan type approximation theorems for product sets and graphs, advancing complex analysis in multiple dimensions.

## Contribution

It defines a novel subalgebra $A_{D}(K)$ that extends Mergelyan approximation results to higher dimensions and more complex structures.

## Key findings

- Established Mergelyan type theorems for product sets in several complex variables.
- Extended approximation results to graphs of functions in complex spaces.
- Provided a new algebraic framework for complex approximation theory.

## Abstract

For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.