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Advances in Analysis and Geometry

New Developments Using Clifford Algebras

  • Book
  • © 2004

Overview

Editors:
  1. Tao Qian

    1. Faculty of Science and Technology, University of Macau, Macau, China

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  2. Thomas Hempfling

    1. Basel, Switzerland

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  3. Alan McIntosh

    1. Centre for Mathematics and its Applications Mathematical Sciences Institute, Australian National University, Canberra, Australia

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  4. Frank Sommen

    1. Department of Mathematical Analysis, University of Ghent, Ghent, Belgium

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  • Contains most recent results and surveys of the state of the art in the discipline
  • Based on an ICM 2002 Satellite Meeting on Clifford Analysis and Its Applications in Macau

Part of the book series: Trends in Mathematics (TM)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xv
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  2. Differential Equations and Operator Theory

    1. Front Matter

      Pages 1-1
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    2. Hodge Decompositions on Weakly Lipschitz Domains

      • Andreas Axelsson, Alan McIntosh
      Pages 3-29

    3. Monogenic Functions of Bounded Mean Oscillation in the Unit Ball

      • Swanhild Bernstein
      Pages 31-50

    4. Bp,q-Functions and their Harmonic Majorants

      • S. Bernstein, K. Gürlebeck, L. F. Reséndis, Luis M. Tovar S.
      Pages 51-63

    5. Spherical Means and Distributions in Clifford Analysis

      • Fred Brackx, Richard Delanghe, Frank Sommen
      Pages 65-96

    6. Hypermonogenic Functions and their Cauchy-Type Theorems

      • Sirkka-Liisa Eriksson, Heinz Leutwiler
      Pages 97-112

    7. On Series Expansions of Hyperholomorphic Bq Functions

      • K. Gürlebeck, A. El-Sayed Ahmed
      Pages 113-129

    8. Pointwise Convergence of Fourier Series on the Unit Sphere of R4 with the Quaternionic Setting

      • Shuang Liu, Tao Qian
      Pages 131-147

    9. Cauchy Kernels for some Conformally Flat Manifolds

      • John Ryan
      Pages 149-160

    10. Clifford Analysis on the Space of Vectors, Bivectors and ℓ-vectors

      • Irene Sabadini, Frank Sommen
      Pages 161-185

  3. Global Analysis and Differential Geometry

    1. Front Matter

      Pages 187-187
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    2. Universal Bochner-Weitzenböck Formulas for Hyper-Kählerian Gradients

      • Yasushi Homma
      Pages 189-208

    3. Cohomology Groups of Harmonic Spinors on Conformally Flat Manifolds

      • Tosiaki Kori
      Pages 209-225

    4. Spin Geometry, Clifford Analysis, and Joint Seminormality

      • Mircea Martin
      Pages 227-255

    5. A Mean Value Laplacian for Strongly Kähler-Finsler Manifolds

      • Zhong Chunping, Zhong Tongde
      Pages 257-286
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Keywords

About this book

On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations ·2 ·2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized complex numbers (hypercomplex numbers) of the form a + bi + cj. It hence took him a long time to accept that a fourth dimension was necessary and that commutativity couldn't be kept and he wondered about a possible real life meaning of this fourth dimension which he identified with the scalar part qo as opposed to the vector part ql i + q2j + q3k which represents a point in space.

Editors and Affiliations

  • Faculty of Science and Technology, University of Macau, Macau, China

    Tao Qian

  • Basel, Switzerland

    Thomas Hempfling

  • Centre for Mathematics and its Applications Mathematical Sciences Institute, Australian National University, Canberra, Australia

    Alan McIntosh

  • Department of Mathematical Analysis, University of Ghent, Ghent, Belgium

    Frank Sommen

Bibliographic Information

  • Book Title: Advances in Analysis and Geometry

  • Book Subtitle: New Developments Using Clifford Algebras

  • Editors: Tao Qian, Thomas Hempfling, Alan McIntosh, Frank Sommen

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7838-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2004

  • Hardcover ISBN: 978-3-7643-6661-2Published: 23 April 2004

  • Softcover ISBN: 978-3-0348-9589-7Published: 29 October 2012

  • eBook ISBN: 978-3-0348-7838-8Published: 06 December 2012

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: XV, 376

  • Topics: Algebra, Analysis, Integral Equations, Operator Theory, Special Functions, Number Theory

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