On spectral analysis of a magnetic Schrodinger operator on planar mixed automorphic forms

TL;DR

This paper characterizes planar mixed automorphic forms related to magnetic Schrödinger operators, revealing their spectral properties and introducing generalized Hermite-type polynomials.

Contribution

It provides a new characterization of mixed automorphic forms via transforms and explores spectral properties of magnetic Schrödinger operators acting on them.

Findings

Spectral properties of magnetic Schrödinger operators are analyzed.

Mixed automorphic forms are characterized as transformed classical automorphic forms.

Introduction of generalized Hermite-type polynomials related to the spectral analysis.

Abstract

We characterize the space of the so-called planar mixed automorphic forms of type $(\nu,\mu)$ with respect to an equivariant pair $(\rho,\tau)$ as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrodinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of Hermite type.