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A pseudo-differential calculus on graded nilpotent Lie groups. (English) Zbl 1319.35316
Ruzhansky, Michael (ed.) et al., Fourier analysis. Pseudo-differential operators, time-frequency analysis and partial differential equation. Based on the presentations at the international conference, Aalto University, near Helsinki, Finland, June 25–29, 2012. Cham: Birkhäuser/Springer (ISBN 978-3-319-02549-0/hbk; 978-3-319-02550-6/ebook). Trends in Mathematics, 107-132 (2014).
Summary: In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantization given by the representation theory. They form an algebra of operators which shares many properties with the usual Hörmander calculus.
For the entire collection see [Zbl 1281.35002].

35S05 Pseudodifferential operators as generalizations of partial differential operators
43A80 Analysis on other specific Lie groups
22E25 Nilpotent and solvable Lie groups
22E30 Analysis on real and complex Lie groups
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