Lower bounds for Riesz-Fischer maps in rigged Hilbert spaces

TL;DR

This paper investigates Riesz-Fischer maps in rigged Hilbert spaces, establishing a key inequality that guarantees the invertibility of the synthesis operator, thus extending the understanding of these sequences in distribution spaces.

Contribution

It introduces a new characterization inequality for Riesz-Fischer maps, ensuring the synthesis operator's continuous inverse in rigged Hilbert spaces.

Findings

Established a key inequality for Riesz-Fischer maps

Proved the existence of a continuous inverse for the synthesis operator

Extended Riesz-Fischer sequence concepts to distribution spaces

Abstract

This note concerns a further study about Riesz-Fischer maps, already introduced by the author in a recent work, that is a notion that extends to the spaces of distributions the sequences that are known as Riesz-Fischer sequences. In particular it is proved a characterizing inequality that have as consequence the existence of the continuous inverse of the synthesis operator.