Ψ-weighted Cauchy-Riemann operators and some associated integral representation. Issue 3 (3rd March 2020)

• Record Type: Journal Article
• Authors: Ariza, Eusebio; Di Teodoro, Antonio; Vanegas, Carmen Judith
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 3(2020)
• Page Start: 335
• Page End: 360
• Publication Date: 2020-03-03
• Subjects: 30E20 -- 45E05 -- 34G10 -- 47D09; Weighted Cauchy-Riemann operator -- Cauchy integral formula -- Cauchy-Pompeiu integral formula -- elliptic operator; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1574928
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: In the present work we introduce a weighted Cauchy-Riemann type operator in the complex plane, where the weights are complex non-constant functions. We construct a fundamental solution for this operator where the weights are complex constant functions and orthogonal functions inspired by the idea for the construction of the Levy function proposed by Miranda (see [23]). Therefore we obtain a Cauchy-Pompeiu integral representation formula. We also present some examples of such representations when we take some particular weights.