Bargmann-Dirichlet Spaces from Magnetic Laplacians and theirs Bargmann Transforms

TL;DR

This paper characterizes Bargmann-Dirichlet spaces as harmonic spaces of magnetic Laplacians and develops associated Bargmann-type transforms, providing new insights into their structure and analysis.

Contribution

It introduces a novel characterization of Bargmann-Dirichlet spaces via magnetic Laplacians and constructs new Bargmann-type integral transforms.

Findings

Bargmann-Dirichlet spaces are harmonic spaces of magnetic Laplacians.

New unitary integral transforms of Bargmann type are developed.

Provides a deeper understanding of the structure of these function spaces.

Abstract

We reconsider the Bargmann-Dirichlet space on the complex plane $\mathbb{C}$ and its generalizations considered in [8]. Concretely, we first present a new characterization of such spaces as harmonic spaces of the magnetic Laplacian with suitable domains. Then, we elaborate an associated unitary integral transforms of Bargmann type.