Complex analysis nowadays has higher-dimensional analoga: the algebra of complex
numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford …

The theory of reproducing kernels started with two papers of 1921 [449] and 1922 [45] which
dealt with typical reproducing kernels of Szegö and Bergman, and since then the theory has …

This article has a twofold purpose: on one hand, we deepen the study of slice regular
functions by studying their behaviour with respect to the so-called C-property and anti-C …

Die Funktionentheorie, im englischen Sprachraum auch Komplexe Analysis genannt, hat in
ihrer mehr als 200jährigen Geschichte eine Vielzahl tiefliegender und ästhetischer …

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 …

This book describes the basic theory of hypercomplex-analytic automorphic forms and
functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces …

In this article we deepen the study of the Bergman theory in the slice regular setting by
providing a description of the Bergman projection and by considering a subclass of slice …

We continue the study of Bergman theory for the class of slice regular functions. In the slice
regular setting there are two possibilities to introduce the Bergman spaces, that are called of …

Cotangent type functions in R n are used to construct Cauchy kernels and Green kernels on
the conformally flat manifolds R n/Zk where 1≤ k≤ n. Basic properties of these kernels are …

Monogenic orthogonal polynomials over 3D prolate spheroids were previously introduced
and shown to have some remarkable properties. In particular, the underlying functions take …