{"title":"Regular Functions on the Scaled Hypercomplex Numbers","authors":"Daniel Alpay, Ilwoo Cho","doi":"10.1007/s00020-024-02756-9","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the regularity of <span>\\(\\mathbb {R}\\)</span>-differentiable functions on open connected subsets of the scaled hypercomplex numbers <span>\\(\\left\\{ \\mathbb {H}_{t}\\right\\} _{t\\in \\mathbb {R}}\\)</span> by studying the kernels of suitable differential operators <span>\\(\\left\\{ \\nabla _{t}\\right\\} _{t\\in \\mathbb {R}}\\)</span>, up to scales in the real field <span>\\(\\mathbb {R}\\)</span>.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"40 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integral Equations and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00020-024-02756-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the regularity of \(\mathbb {R}\)-differentiable functions on open connected subsets of the scaled hypercomplex numbers \(\left\{ \mathbb {H}_{t}\right\} _{t\in \mathbb {R}}\) by studying the kernels of suitable differential operators \(\left\{ \nabla _{t}\right\} _{t\in \mathbb {R}}\), up to scales in the real field \(\mathbb {R}\).
期刊介绍：
Integral Equations and Operator Theory (IEOT) is devoted to the publication of current research in integral equations, operator theory and related topics with emphasis on the linear aspects of the theory. The journal reports on the full scope of current developments from abstract theory to numerical methods and applications to analysis, physics, mechanics, engineering and others. The journal consists of two sections: a main section consisting of refereed papers and a second consisting of short announcements of important results, open problems, information, etc.
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