2024/04/03 by Daniel Alpay, Alpay, Daniel, Ilwoo Cho +3
Economics, Econometrics and Finance · Mathematics · #30G35 #46E22 #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2404.03065
openalex publication_date 2024/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbers ℍt, t∈ℝ^*, of which the ℍ-1=ℍ is the space of quaternions and ℍ1 is the space of split quaternions. We also describe the scaled Fueter-type variables associated to these operators, developing a coherent theory in this field. We use these types of variables to build different types of function spaces on ℍt. Counterparts of the Hardy space and of the Arveson space are also introduced and studied in the present setting. The two different adjoints in the scaled hypercomplex numbers lead to two parallel cases in each instance. Finally we introduce and study the notion of rational function.