Contractive projections in Paley-Wiener spaces

TL;DR

This paper characterizes when the canonical projection in Paley-Wiener spaces, associated with disjoint unions of parallelepipeds, acts as a contraction, based on set and exponent conditions.

Contribution

It provides necessary and sufficient conditions for the projection to be a contraction in Paley-Wiener spaces with specific geometric and exponent parameters.

Findings

Identifies conditions for contraction in Paley-Wiener projections

Characterizes geometric and exponent relations for contraction

Advances understanding of projections in harmonic analysis

Abstract

Let $S_1$ and $S_2$ be disjoint finite unions of parallelepipeds. We describe necessary and sufficient conditions on the sets $S_1,S_2$ and exponents $p$ such that the canonical projection $P$ from $PW_{S_1\cup S_2}^p$ to $PW_{S_1}^p$ is a contraction.