2018/05/26 by Elifalet López‐González, Elifalet López-González, López-González, Elifalet · 1 citation
Mathematics · #30G35 #31A30 #35J30 #35N05 #35N99 #58C20 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CA #msc:30G35 #msc:31A30 #msc:35J30 #msc:35N05 #msc:35N99 #msc:58C20
paper · pdf · doi:10.48550/arxiv.1805.10524
An updated version of the manuscript is presented
openalex publication_date 2018/05/26 · arxiv created 2021/04/23 · arxiv updated 2021/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the \emphφ\mathbbA-differentiability for functions f:U⊂ \mathbb Rk→\mathbb A where \mathbb A is the linear space \mathbb Rn endowed with an algebra product which is unital, associative, commutative, U is an open set, and φ:U⊂ \mathbb Rk→\mathbb A is a differentiable function in the usual sense. We also introduce the corresponding generalized Cauchy-Riemann equations (φ\mathbbA-CREs), the Cauchy-integral theorem, and the φ\mathbb A-differential equations. The four-dimensional vector fields associated with triangular billiards are φ\mathbbA-differentiable. The φ\mathbb A-differential equations can be used for constructing exact solutions of partial differential equations like the three-dimensional heat equation.