Trends in Mathematics

Advances in Analysis and Geometry

New Developments Using Clifford Algebras

Editors: Qian, T., Hempfling, Th., McIntosh, A., Sommen, F. (Eds.)

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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.

Table of contents (18 chapters)

  • Hodge Decompositions on Weakly Lipschitz Domains

    Axelsson, Andreas (et al.)

    Pages 3-29

  • Monogenic Functions of Bounded Mean Oscillation in the Unit Ball

    Bernstein, Swanhild

    Pages 31-50

  • Bp,q-Functions and their Harmonic Majorants

    Bernstein, S. (et al.)

    Pages 51-63

  • Spherical Means and Distributions in Clifford Analysis

    Brackx, Fred (et al.)

    Pages 65-96

  • Hypermonogenic Functions and their Cauchy-Type Theorems

    Eriksson, Sirkka-Liisa (et al.)

    Pages 97-112

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-7838-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-7643-6661-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-9589-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advances in Analysis and Geometry
Book Subtitle
New Developments Using Clifford Algebras
Editors
  • Tao Qian
  • Thomas Hempfling
  • Alan McIntosh
  • Franciscus Sommen
Series Title
Trends in Mathematics
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-7838-8
DOI
10.1007/978-3-0348-7838-8
Hardcover ISBN
978-3-7643-6661-2
Softcover ISBN
978-3-0348-9589-7
Series ISSN
2297-0215
Edition Number
1
Number of Pages
XV, 376
Topics