A unified theory of regular functions of a hypercomplex variable

[2408.01523] A unified theory of regular functions of a hypercomplex variable Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Complex Variables arXiv:2408.01523 (math) [Submitted on 2 Aug 2024 ( v1 ), last revised 30 Jan 2026 (this version, v2)] Title: A unified theory of regular functions of a hypercomplex variable Authors: Riccardo Ghiloni , Caterina Stoppato View a PDF of the paper titled A unified theory of regular functions of a hypercomplex variable, by Riccardo Ghiloni and 1 other authors View PDF HTML (experimental) Abstract: This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises Fueter-regular functions, slice-regular functions and a recently-discovered function class. In the special case of Clifford-valued functions of one paravector variable, it encompasses monogenic functions, slice-monogenic functions, generalized partial-slice monogenic functions, and a variety of function classes not yet considered in literature. For $T$-regular functions over an associative $*$-algebra, this work provides integral formulas, series expansions, an Identity Principle, a Maximum Modulus Principle and a Representation Formula. It also proves some foundational results about $T$-regular functions over an alternative but nonassociative $*$-algebra, such as the real algebra of octonions. Comments: 76 pages, to appear in the Bulletin des Sciences Mathématiques Subjects: Complex Variables (math.CV) MSC classes: 30G35 (Primary) 16P10, 17D05 (Secondary) Cite as: arXiv:2408.01523 [math.CV] (or arXiv:2408.01523v2 [math.CV] for this version) https://doi.org/10.48550/arXiv.2408.01523 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Bull. Sci. Math., 209:103794 (2026) Related DOI : https://doi.org/10.1016/j.bulsci.2026.103794 Focus to learn more DOI(s) linking to related resources Submission history From: Caterina Stoppato [ view email ] [v1] Fri, 2 Aug 2024 18:30:41 UTC (60 KB) [v2] Fri, 30 Jan 2026 16:59:21 UTC (62 KB) Full-text links: Access Paper: View a PDF of the paper titled A unified theory of regular functions of a hypercomplex variable, by Riccardo Ghiloni and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2024-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Special Markowitz: Thermodynamic Formalism for the Joint Regularisation of Returns and Covariance#1136553
• Hyperfunction quantum field theory: Localized fields without localized test functions#498653
• Matter power spectrum from a Lagrangian-space regularization of perturbation theory#1053391
• Regularization in quantum field theory from the causal point of view#498808
• On the regularity of solutions to the Hamilton-Jacobi equations for the N-body problem#454639