Pseudo-differential Operators on SU(2)

  • Michael Ruzhansky
  • Ville Turunen
Part of the Pseudo-Differential Operators book series (PDO, volume 2)


In this chapter we carry out the analysis of operators on SU(2) with an application to the operators on the three-dimensional sphere \( \mathbb{S}^3 \). In particular, we derive a much simpler symbolic characterisation of pseudo-differential operators on SU(2) than the one given in Definition 10.9.5. In turn, this will also yield a characterisation of full symbols of pseudo-differential operators on the 3-sphere \( \mathbb{S}^3 \). We note that this approach works globally on the whole sphere, since the version of the Fourier analysis that we use is different from the one in, e.g., [110, 122, 111] which covers only a hemisphere, with singularities at the equator. For a general introduction and motivation for the analysis on SU(2) we refer the reader to the introduction in Part IV where the cases of SU(2) and \( \mathbb{S}^3 \) were put in a perspective.


Continuous Linear Operator Standard Matrix Full Symbol Symbol Class Involutive Algebra 
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Copyright information

© Birkhäuser Verlag AG 2010

Authors and Affiliations

  • Michael Ruzhansky
    • 1
  • Ville Turunen
    • 2
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Institute of MathematicsHelsinki University of TechnologyFinland

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