Hypercomplex Analysis

This volume contains some papers written by the participants to the Session "Quaternionic and Cli? ord Analysis" of the 6th ISAAC Conference (held in Ankara, Turkey, in August 2007) and some invited contributions. The contents cover several di? erent aspects of the hypercomplex analysis. All contributed - pers represent the most recent achievements in the area as well as "state-of-the art" expositions. The Editors are grateful to the contributors to this volume, as their works show how the topic of hypercomplex analysis is lively and fertile, and to the r- erees, for their painstaking and careful work. The Editors also thank professor M. W. Wong, President of the ISAAC, for his support which made this volume possible. October 2008, Irene Sabadini Michael Shapiro Frank Sommen Quaternionic and Cli? ord Analysis Trends in Mathematics, 1-9 c 2008 Birkh auser Verlag Basel/Switzerland An Extension Theorem for Biregular Functions in Cli? ord Analysis Ricardo Abreu Blaya and Juan Bory Reyes Abstract. In this contribution we are interested in ? nding necessary and s- ? cient conditions for thetwo-sided biregular extendibility of functions de? ned 2n on a surface of R , but the latter without imposing any smoothness requi- ment. Mathematics Subject Classi? cation (2000). Primary 30E20, 30E25; Secondary 30G20. Keywords. Cli? ord analysis, biregular functions, Bochner-Martinelli formulae, extension theorems.

An Extension Theorem for Biregular Functions in Clifford Analysis. - The Hilbert Transform on the Unit Sphere in ? m. - Discrete Clifford Analysis: A Germ of Function Theory. - On Factorization of Bicomplex Meromorphic Functions. - An Overview on Functional Calculus in Different Settings. - A Structure Formula for Slice Monogenic Functions and Some of its Consequences. - On the CK-extension for a Special Overdetermined System in Complex Clifford Analysis. - Polynomial invariants for the rarita-schwinger operator. - Hypermonogenic functions and their dual functions. - Description of a Complex of Operators Acting Between Higher Spinor Modules. - Recent Developments for Regular Functions of a Hypercomplex Variable. - Differential Equations in Algebras. - Necessary and Sufficient Conditions for Associated Pairs in Quaternionic Analysis. - Hyperderivatives in Clifford Analysis and Some Applications to the Cliffordian Cauchy-type Integrals. - Directional quaternionic hilbert operators. - Hilbert Transforms on the Sphere and Lipschitz Surfaces. - n-Dimensional Bloch Classes.