# Holomorphic cohomological convolution and Hadamard product

## TL;DR

This paper explores the relationship between a generalized Hadamard product and holomorphic cohomological convolution on complex numbers, introducing new concepts to extend the product to broader function classes.

## Contribution

It introduces a generalized Hadamard product applicable to functions not vanishing at infinity and defines strongly convolvable sets, linking these to holomorphic cohomological convolution.

## Key findings

- Established a link between Pohlen's extended Hadamard product and cohomological convolution.
- Defined a generalized Hadamard product for broader function classes.
- Introduced the concept of strongly convolvable sets.

## Abstract

In this article, we explain the link between Pohlen's extended Hadamard product and the holomorphic cohomological convolution on $\mathbb{C}^*$. For this purpose, we introduce a generalized Hadamard product, which is defined even if the holomorphic functions do not vanish at infinity, as well as a notion of strongly convolvable sets.