On the structure of analytic vectors for the schrodinger representation

TL;DR

This paper investigates the structure of analytic vectors in Schrödinger representations of the Heisenberg group, employing Hardy's theorem and Hermite expansions to derive precise characterization theorems.

Contribution

It introduces refined Hardy's theorem variants and connects them with Hermite expansions to provide detailed structure theorems for analytic vectors.

Findings

Precise representation theorems for analytic vectors

Connection established between Hardy's theorem and Hermite expansions

Enhanced understanding of the structure of Schrödinger representations

Abstract

This article deals with the structure of analytic and entire vectors for the Schr\"{o}dinger representations of the Heisenberg group. Using refined versions of Hardy's theorem and their connection with Hermite expansions we obtain very precise representation theorems for analytic and entire vectors.