Hypercomplex Analysis / edited by Irene Sabadini, Michael Shapiro, Frank Sommen.

Springer eBooks

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.

This book contains selected papers from the ISAAC conference 2007 and invited contributions. The topics covered represent the main streams of research in hypercomplex analysis as well as "state of the art" expository articles. The book will be of interest to researchers and postgraduate students in various areas of mathematical analysis, e.g. one and several complex variables; PDE; hypercomplex analysis; operator theory; theoretical and mathematics physics.

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