Class of hypocomplex structures on the two dimensional torus

2019/02/11 by Abdelhamid Meziani, Meziani, Abdelhamid, Giuliano Zugliani +1
Mathematics · #35A01 #35C15 #35F05 #58J99 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1902.03922

openalex publication_date 2019/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Hölder solvability of a class of complex vector fields on the torus \mathbbT². We make use of the Theta function to associate a Cauchy-Pompeiu type integral operator. A similarity principle for the solutions of the equation Lu=au+bu is obtained.

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