# Singular Green Operators of Finite Regularity in the Edge Algebra Formalism

## TL;DR

This paper develops a new calculus for parameter-dependent singular Green operators on half-spaces, integrating boundary regularity and edge pseudodifferential techniques for advanced boundary value problem analysis.

## Contribution

It introduces a novel calculus combining Grubb's boundary regularity methods with Schulze's edge pseudodifferential techniques for singular Green operators.

## Key findings

- Unified framework for boundary and edge operators
- Enhanced analysis of boundary value problems with finite regularity
- New tools for parameter-dependent Green operator calculus

## Abstract

We introduce a calculus for parameter-dependent singular Green operators on the half-space $\mathbb{R}^n_+$ that combines both elements of Grubb's calculus for boundary value problems of finite regularity and techniques of Schulze's calculus for pseudodifferential operators on manifolds with edges.