## Clifford Algebra and Spinor-valued Functions: A Function Theory for the Dirac Operator, Volume 1This volume describes the substantial developments in Clifford analysis which have taken place during the last decade and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (chapters 0 and 1) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters 2 and 3 illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. |

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### Contents

Editors Preface | 7 |

Clifford algebras over lower dimensional Euclidean spaces | 11 |

2 | 33 |

Copyright | |

10 other sections not shown

### Other editions - View all

Clifford Algebra and Spinor-valued Functions: Disk Richard Delanghe,F. Sommen,V. Souček No preview available - 1992 |

Clifford Algebra and Spinor-Valued Functions Sylvia Delanghe,F. Sommen,Vladimir Soucek No preview available - 2014 |

### Common terms and phrases

analysis analytic associative algebra basic basis belongs bundle C-valued called Cauchy clearly Clifford algebra coefficients compact complex compute Consequently consider converges corresponding decomposition defined definition denoted described determined differential dimension Dirac operator domain element equation Example exists expression extended fact Finally fixed follows formula Furthermore given hand Hence holomorphic homogeneous identified implies inner integral introduced inverse isomorphic isotropic Laurent Lemma linear M+(k matrix means monogenic functions Moreover multiplication namely neighbourhood Notice obtain operator oriented orthogonal plane polynomial of degree polynomials projection Proof properties prove pure spinors relation Remark representation residue respectively restriction Rm+1 rotation satisfying separately solutions space spherical monogenics spinor subset subspace taking Taylor Theorem transform unique values vector vector space whence written