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Quantization on graded Lie groups

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

Abstract

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.

Keywords

Sobolev Space Functional Calculus Smooth Vector Convolution Kernel Sobolev Norm 
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Copyright information

© The Author(s) 2016

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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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