$ {C}^2(\mathbb{R}^2) $ Nonnegative Extension by Bounded-depth Operators

TL;DR

This paper establishes the existence of a nonlinear, nonnegative $ C^2(R^2) $ extension operator with bounded depth, advancing the mathematical understanding of extension problems in analysis.

Contribution

It introduces a new nonlinear extension operator that is nonnegative, parameter-dependent, and has bounded depth, filling a gap in extension theory.

Findings

Existence of a nonlinear $ C^2(R^2) $ extension operator.

Operator is nonnegative and parameter-dependent.

Operator has bounded depth.

Abstract

In this paper, we prove the existence of a nonnegative parameter-dependent (nonlinear) $ C^2(\mathbb{R}^2) $ extension operator with bounded depth.