Miller, Kenneth G. Invariant pseudodifferential operators on two step nilpotent Lie groups. II. (English) Zbl 0662.35127 Mich. Math. J. 33, 395-401 (1986). [For part I see ibid. 29, 315-328 (1982; Zbl 0524.35102).] In a previous paper by the author [Trans. Am. Math. Soc. 280, 721-736 (1983; Zbl 0545.35098)] a method was given for constructing parametrices and inverses for invariant hypoelliptic pseudodifferential operators which are homogeneous with respect to the natural dilations on a step two nilpotent Lie group. The construction made use of a calculus for invariant pseudodifferential operators described in part I. It is shown here that a similar calculus is also valid in the case of arbitrary dilations on a step two group. The parametrix construction of the above cited paper can then be easily extended to include operators homogeneous with respect to arbitrary dilations. As noted in a paper by the author [Contemp. Math. 27, 231-235 (1984; Zbl 0541.35018)], this construction can be “microlocalized”. Cited in 2 Documents MSC: 35S05 Pseudodifferential operators as generalizations of partial differential operators 65H10 Numerical computation of solutions to systems of equations 47A60 Functional calculus for linear operators 22E25 Nilpotent and solvable Lie groups Keywords:parametrices; inverses; invariant hypoelliptic pseudodifferential operators; homogeneous; step two nilpotent Lie group; calculus; microlocalized Citations:Zbl 0524.35102; Zbl 0545.35098; Zbl 0541.35018 PDFBibTeX XMLCite \textit{K. G. Miller}, Mich. Math. J. 33, 395--401 (1986; Zbl 0662.35127) Full Text: DOI