Quantization on graded Lie groups

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


In this chapter we develop the theory of pseudo-differential operators on graded Lie groups. Our approach relies on using positive Rockland operators, their fractional powers and their associated Sobolev spaces studied in Chapter 4. As we have pointed out in the introduction, the graded Lie groups then become the natural setting for such analysis in the context of general nilpotent Lie groups.


Sobolev Space Functional Calculus Smooth Vector Convolution Kernel Sobolev Norm 
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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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