Pseudodifferential operators on groups with dilations (Q1202445)

The authors consider a general pseudodifferential calculus defined on an homogeneous nilpotent group. In comparison with previous works of a lot of authors (for example \textit{G. B. Folland} and \textit{E. M. Stein} [Commun. Pure Appl. Math. 27, 429-522 (1974; Zbl 0293.35012)]; \textit{L. P. Rothschild} and \textit{E. M. Stein} [Acta Math. 137(1976), 247-320 (1977; Zbl 0346.35030)]; \textit{A. Melin} [Ann. Global Anal. Geom. 1, No. 1, 79- 130 (1983; Zbl 0524.58044)]) the authors present general criteria for the existence of parametrices, as well as explicit product and adjoint formulas. In particular, the authors obtain new generalizations of the Rockland's conjecture which was proved by the reviewer and \textit{J. Nourrigat} in the case of left invariant homogeneous different operators on graded nilpotent groups [Commun. Partial Differ. Equations 4, 899-958 (1979; Zbl 0423.35040)] and extended further by \textit{P. Głowacki} [Stud., Math. 98, No. 2, 98-114 (1991; Zbl 0737.43002)].