Pseudo-differential operators on the Heisenberg group

  • Veronique Fischer
  • Michael Ruzhansky
Open Access
Part of the Progress in Mathematics book series (PM, volume 314)


The Heisenberg group was introduced in Example 1.6.4. It was our primal example of a stratified Lie group, see Section 3.1.1. Due to the importance of the Heisenberg group and of its many realisations, we start this chapter by sketching various descriptions of the Heisenberg group. We also describe its dual via the well known Schrödinger representations. Eventually, we particularise our general approach given in Chapter 5 to the Heisenberg group.


Sobolev Space Heisenberg Group Linear Continuous Operator Schwartz Space Canonical Commutation Relation 
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Authors and Affiliations

  • Veronique Fischer
    • 1
  • Michael Ruzhansky
    • 2
  1. 1.Department of MathematicsUniversity of BathBathUK
  2. 2.Department of MathematicsImperial College LondonLondonUK

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