Results 221 to 230 of about 21,179 (236)

Growth of Entire Slice Regular Functions

2016
In this chapter we study the growth of entire slice regular functions and we relate it with the coefficients of the power series expansion of a function. We prove some brand new results, like the Jensen and Caratheodory theorem. These results are not immediate extensions of the analogous results in the complex setting.
Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa   +2 more
openaire   +1 more source

Slice regular functions of several Clifford variables

AIP Conference Proceedings, 2012
We introduce a class of slice regular functions of several Clifford variables. Our approach to the definition of slice functions is based on the concept of stem functions of several variables and on the introduction on real Clifford algebras of a family of commuting complex structures.
Ghiloni, Riccardo, Perotti, Alessandro
openaire   +2 more sources

On Two Approaches to the Bergman Theory for Slice Regular Functions

2013
In this paper we show that the classical Bergman theory admits two possible settings for the class of slice regular functions. Let Ω be a suitable open subset of the space of quaternions ℍ that intersects the real line and let \(\mathbb{S}^{2}\) be the unit sphere of purely imaginary quaternions.
COLOMBO, FABRIZIO, J. O. Gonzalez Cervantes, M. E. Luna Elizarraras, SABADINI, IRENE MARIA, M. Shapiro   +4 more
openaire   +1 more source

On Cauchy Integral Theorem for Quaternionic Slice Regular Functions

Complex Analysis and Operator Theory, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Approximation of Slice Regular Functions in Compact Sets

2019
In this chapter, we present the counterparts in the slice regular setting of some classical results in complex analysis, namely approximation results of Runge type, Mergelyan type and Arakelian type. Then, we study approximation by quaternionic Faber polynomials and by quaternionic polynomials in Bergman spaces.
Sorin G. Gal, Irene Sabadini
openaire   +1 more source

Fueter Regularity and Slice Regularity: Meeting Points for Two Function Theories

2013
We present some meeting points between two function theories, the Fueter theory of regular functions and the recent theory of quaternionic slice regular functions, which includes polynomials and power series with quaternionic coefficients. We show that every slice regular function coincides up to the first order with a unique regular function on the ...
openaire   +2 more sources

Almansi-type theorems for slice-regular functions on Clifford algebras

Complex Variables and Elliptic Equations, 2021
Alessandro Perotti
exaly  

Quaternionic slice regular functions with some sphere bundles

Complex Variables and Elliptic Equations, 2022
J OSCAR González-Cervantes
exaly  

The C-property for slice regular functions and applications to the Bergman space

Complex Variables and Elliptic Equations, 2013
Fabrizio Colombo, J OSCAR González-Cervantes, Irène Sabadini   +2 more
exaly  

Global differential equations for slice regular functions

Mathematische Nachrichten, 2014
Riccardo Ghiloni, Alessandro Perotti
exaly