Pseudo-differential Operators on ℝn

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


The subject of pseudo-differential operators on ℝ n is well studied and there are many excellent monographs on the subject, see, e.g., [27, 33, 55, 71, 101, 112, 130, 135, 152], as well as on the more general subject of Fourier integral operators, microlocal analysis, and related topics in, e.g., [30, 56, 45, 81, 113]. Therefore, here we only sketch main elements of the theory. In this chapter, we use the notation 〈ξ〉 = (1 + |ξ|2)1/2.


Asymptotic Expansion Sobolev Space Asymptotic Formula Inverse Fourier Transform Integral 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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