Integral formulas of the Hilbert, Poincaré-Bertrand, Schwarz and Poisson type for the β–analytic function theory

Juan Bory-Reyes, Ricardo Abreu-Blaya, Marco Antonio Pérez-de la Rosa, Baruch Schneider

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Abstract

In the present work we obtain some analogues of the Hilbert formulas on the unit circle and on the upper half-plane for the theory of solutions of a special case of the Beltrami equation in C to be referred as β-analytic functions. Furthermore, a Poincaré–Bertrand formula related to the β-Cauchy singular integral over a closed Jordan curve is derived and it is used to derive the corresponding Schwarz and Poisson formulas.

Original languageEnglish
Article number124493
JournalJournal of Mathematical Analysis and Applications
Volume492
Issue number2
DOIs
StatePublished - 15 Dec 2020

Keywords

  • Hilbert formulas
  • Poincaré–Bertrand formulas
  • Poisson formulas
  • Schwarz formulas
  • β–analytic functions

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