## 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

Euclidean mspace | 12 |

Clifford Algebras and Spinor Spaces | 48 |

Monogenic functions | 129 |

Copyright | |

8 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 associative algebra basic basis belongs bundle C-valued called Cauchy clearly Clifford algebra coefficients compact complex compute Consequently consider constructed coordinates corresponding decomposition defined definition denoted described determined differential dimension dimensional 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 invariant inverse isomorphic isotropic Laurent Lemma linear manifold matrix means monogenic functions Moreover multiplication namely neighbourhood Notice obtain operator oriented orthogonal orthonormal basis plane polynomials projection Proof properties prove pure spinors relations Remark representation represented residue respectively restriction Rm+1 rotation satisfying solutions space spinor structure subset subspace taking Theorem theory transform unique unit values vector space whence written