# An algebra of distributions related to a star product with separation of variables

## TL;DR

This paper constructs an algebra of formal distributions at a point on a pseudo-Kähler manifold to analyze formal oscillatory integrals associated with a star product with separation of variables.

## Contribution

It introduces a new algebraic framework for formal distributions linked to star products with separation of variables on pseudo-Kähler manifolds.

## Key findings

- Constructed an associative algebra of formal distributions at a point.
- Expressed formal oscillatory exponents using this algebra.
- Provided tools for analyzing formal oscillatory integrals in deformation quantization.

## Abstract

Given a star product with separation of variables $\star$ on a pseudo-K\"ahler manifold $M$ and a point $x_0 \in M$, we construct an associative algebra of formal distributions supported at $x_0$. We use this algebra to express the formal oscillatory exponents of a family of formal oscillatory integrals related to the star product $\star$.