h-Holomorphic Functions of Double Variable and their Applications

TL;DR

This paper explores h-holomorphic functions of double variables, examining their properties and applications in solving 2D hyperbolic problems in mathematical physics, extending concepts from complex analysis.

Contribution

It introduces and analyzes properties of h-holomorphic functions and their mappings, providing new tools for hyperbolic problem solving in mathematical physics.

Findings

Properties analogous to complex holomorphic functions are established.

h-Conformal mappings are shown to be useful in hyperbolic PDEs.

Applications to 2D hyperbolic problems are demonstrated.

Abstract

The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the properties of general $h$-conformal mappings and the properties of the mappings, which are hyperbolic analogues of complex elementary functions. We discuss the utility of $h$-conformal mappings to solving 2-dimensional hyperbolic problems of Mathematical Physics.