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Fourier Theory Under Möbius Transformations

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Book cover Clifford Algebras and their Applications in Mathematical Physics

Part of the book series: Progress in Physics ((PMP,volume 19))

Abstract

We study Fourier multipliers and singular integrals on curves and surfaces that are Möbius transformation images of Lipschitz graphs and starlike Lipschitz surfaces. We show that the singular integrals in each case form an operator algebra identical to the bounded holomorphic Fourier multipliers and the Cauchy-Dunford bounded holomorphic functional calculus of the associated Dirac operator in the context considered here.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Beijing, 100080, P.R. China

    Xinhua Ji

  2. School of Mathematical and Computer Sciences, The University of New England, Armidale, NSW, 2351, Australia

    Tao Qian

  3. Department of Mathematics, The University of Arkansas, Fayetteville, Arkansas, 72701, USA

    John Ryan

Authors
  1. Xinhua Ji
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  2. Tao Qian
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  3. John Ryan
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Arkansas, Fayetteville, AR, 72701, USA

    John Ryan

  2. Faculty of Mathematics and Informatics, Freiberg University of Mining and Technology, 09596, Freiberg, Germany

    Wolfgang Sprößig

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Ji, X., Qian, T., Ryan, J. (2000). Fourier Theory Under Möbius Transformations. In: Ryan, J., Sprößig, W. (eds) Clifford Algebras and their Applications in Mathematical Physics. Progress in Physics, vol 19. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1374-1_4

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  • DOI: https://doi.org/10.1007/978-1-4612-1374-1_4

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7119-2

  • Online ISBN: 978-1-4612-1374-1

  • eBook Packages: Springer Book Archive

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