## Clifford Analysis and Its ApplicationsF. Brackx, John Stephen roy Chisholm, V. Soucek In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields. |

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### Contents

II | 1 |

III | 9 |

IV | 27 |

V | 39 |

VI | 49 |

VII | 59 |

VIII | 71 |

IX | 81 |

XX | 193 |

XXI | 213 |

XXII | 223 |

XXIII | 231 |

XXIV | 247 |

XXV | 255 |

XXVI | 267 |

XXVII | 283 |

X | 91 |

XI | 103 |

XII | 113 |

XIII | 123 |

XIV | 135 |

XV | 143 |

XVI | 155 |

XVII | 163 |

XVIII | 173 |

XIX | 183 |

XXVIII | 293 |

XXIX | 303 |

XXX | 323 |

XXXI | 341 |

XXXII | 361 |

XXXIII | 377 |

XXXIV | 389 |

XXXV | 399 |

XXXVI | 411 |

### Common terms and phrases

2001 Kluwer Academic 60th birthday abstract analytic Applications boundary value problems Brackx bundle Cauchy Cauchy-Riemann classical Clifford algebra Clifford analysis coefficients compute conformally invariant consider coordinates corresponding Dedicated to Richard defined definition denote differential forms dimension dimensional Dirac operator domain double covers e-mail elements elliptic equation Euclidean field finite formula Fredholm function f geometry Giirlebeck given Hardy spaces harmonic Hilbert holomorphic homogeneous hypercomplex hyperholomorphic introduced invariant differential operators invariant operators irreducible isomorphism kernel Kluwer Academic Publishers LEMMA Lie algebra linear Lipschitz Lipschitz domains Malonek manifold mapping Math Mathematics Subject Classification matrix metaplectic monogenic functions obtained orthogonal parabolic plane polynomials projection proof properties quaternionic relations representation resolution result Rham Riccati Richard Delanghe satisfying scalar singular integral singular integral operators solutions Sommen spacetime spherical spin spin group spinor subspace symplectic syzygies tensor theorem theory transform vector variables wavelets

### References to this book

Advances in Analysis and Geometry: New Developments Using Clifford Algebras Tao Qian Limited preview - 2004 |