Generalized partial-slice monogenic functions

Abstract

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been studied. The main purpose of this article is to describe a new function theory which includes both of them as special cases. This theory allows to prove nice properties such as the identity theorem, a Representation Formula, the Cauchy (and Cauchy-Pompeiu) integral formula, the maximum modulus principle, a version of the Taylor and Laurent series expansions. As a complement, we shall also offer two approaches to these functions via slice functions and via global differential operators. In addition, we discuss the conformal invariance property under a proper group of Möbius transformations preserving the partial symmetry of the involved domains.

To appear in Transactions of the American Mathematical Society

References in corpus (3)

• Slice regular functions on real alternative algebras
• A new series expansion for slice regular functions
• Slice regularity and harmonicity on Clifford algebras

Cited by in corpus (4)

• On the Fueter-Sce theorem for generalized partial-slice monogenic functions
• A unified theory of regular functions of a hypercomplex variable
• A manifold Fueter-Sce phenomenon in one hypercomplex variable
• Segal-Bargmann transform for generalized partial-slice monogenic functions