Open Access 2016 | OriginalPaper | Chapter
Quantization on graded Lie groups
Authors : Veronique Fischer, Michael Ruzhansky
Published in: Quantization on Nilpotent Lie Groups
Publisher: Springer International Publishing
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.