The Mittag-Leffler Theorem for regular functions of a quaternionic variable
Graziano Gentili, Giulia Sarfatti
TL;DR
This paper extends the classical Mittag-Leffler Theorem to regular functions of quaternionic variables, utilizing a new notion of principal part inspired by spherical analyticity.
Contribution
It introduces a quaternionic version of the Mittag-Leffler Theorem based on a novel concept of principal part aligned with spherical analyticity.
Findings
Established a quaternionic Mittag-Leffler Theorem
Defined a new notion of principal part for quaternionic functions
Connected spherical analyticity with classical complex analysis
Abstract
We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · Matrix Theory and Algorithms