Bicomplex Schwarz and Dirichlet Boundary Value Problems

2025/07/21 by Blair, William L. · 1 citation
#30E25 #30G30 #30J99 #35C15 #46F20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.15653

Abstract

We define and solve boundary value problems of Schwarz and Dirichlet type on the complex unit disk for bicomplex-valued functions.

Citations

• An Atomic Representation for Bicomplex Hardy Classes
• Bergman spaces for the bicomplex Vekua equation with bounded coefficients
• Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients

Cited by

• Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem

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