Presents integral formulas and series expansions for monogenic functions in real alternative *-algebras that unify several hypercomplex analysis theories.
A unified theory of regular functions of a hypercomplex variable
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
fields
math.CV 3years
2025 3verdicts
UNVERDICTED 3representative citing papers
Initiates monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli, Plemelj-Sokhotski, and Hartogs extension results in this unified setting.
Generalized partial-slice monogenic functions are introduced over octonions, unifying regular and slice regular functions with proofs of identity theorem, representation formula, Cauchy integral formula, maximum modulus principle, Fueter polynomials, and Taylor series.
citing papers explorer
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Monogenic functions over real alternative *-algebras: fundamental results and applications
Presents integral formulas and series expansions for monogenic functions in real alternative *-algebras that unify several hypercomplex analysis theories.
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Monogenic functions over real alternative *-algebras: the several hypercomplex variables case
Initiates monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli, Plemelj-Sokhotski, and Hartogs extension results in this unified setting.
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Generalized partial-slice monogenic functions: the octonionic case
Generalized partial-slice monogenic functions are introduced over octonions, unifying regular and slice regular functions with proofs of identity theorem, representation formula, Cauchy integral formula, maximum modulus principle, Fueter polynomials, and Taylor series.