Modulation spaces with scaling symmetry

TL;DR

This paper introduces a new family of modulation spaces that exhibit scaling symmetry and examines how Schrödinger multipliers act on these spaces, providing insights into their structure and properties.

Contribution

The paper constructs a novel class of modulation spaces with inherent scaling symmetry and analyzes the behavior of Schrödinger multipliers on them, advancing understanding of their functional framework.

Findings

Construction of modulation spaces with scaling symmetry

Analysis of Schrödinger multiplier behavior on these spaces

Insights into the structure of modulation spaces

Abstract

We indicate how to construct a family of modulation function spaces that have a scaling symmetry. We also illustrate the behavior of the Schr\"odinger multiplier on such function spaces.