Novel Results on Homogenous Bicomplex Banach Modules with Hyperbolic-Valued Norm
Proceedings of the National Academy of Sciences India Section A - Physical Sciences, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.1007/s40010-026-01006-4
- Journal Name: Proceedings of the National Academy of Sciences India Section A - Physical Sciences
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, INSPEC, MathSciNet, zbMATH, Technology Collection (ProQuest)
- Keywords: Bicomplex Lebesgue space, Bicomplex Lipschitz spaces, Convolution, Homogenous bicomplex Banach modules, Locally compact abelian groups
- Ondokuz Mayıs University Affiliated: Yes
Abstract
The initial phase of this research involves the examination of the properties of space, for, using the -Haar measure on the locally compact abelian group G. It is demonstrated that is a -normed bicomplex Banach algebra with bounded approximate identity. Then, as an extension of the well-known Lipschitz spaces, bicomplex Lipschitz spaces are presented. The bicomplex versions of semi homogeneous and homogeneous Banach spaces are defined as semi-homogeneous bicomplex Banach-modules and homogeneous bicomplex Banach-modules, respectively. Numerous properties of these modules are investigated.