Complex Creation Operator and Planar Automorphic Functions

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2023-11-01 DOI:10.1007/s11040-023-09471-8

Ghanmi Allal, Imlal Lahcen

引用次数: 0

Abstract

We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell–Humbert automorphy factor, arising as images of the holomorphic ones by means of the creation differential operator. This is closely connected to the spectral theory of the magnetic Laplacian on the complex plane.

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复生成算子与平面自同构函数

我们给出了多解析平面自同构函数的一个具体的表征，这是一类特殊的非解析平面自同构函数，它们是通过创建微分算子作为全纯自同构函数的像而产生的，与apell - humbert自同构因子有关。这与复平面上磁拉普拉斯的谱理论密切相关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.