Pseudo-differential Operators on Homogeneous Spaces

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


In this chapter we discuss pseudo-differential operators on homogeneous spaces. The main question addressed here is how operators on such a space are related to pseudo-differential operators on the group that acts on the space. Once such a correspondence is established, one can use it to map the whole construction developed earlier from the group to the homogeneous space. We also note that among other things, this chapter provides an application to the characterisation of pseudo-differential operators in terms of Σ m -classes in Theorem 10.9.6. An important class of examples to keep in mind here are the spheres \( \mathbb{S}^n \cong SO(n)\backslash SO(n + 1) \cong SO(n + 1)/SO(n) \).


Homogeneous Space Open Cover Maximal Torus Fourier Integral Operator Schwartz Kernel 
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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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