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A groupoid approach to pseudodifferential calculi. (English) Zbl 1433.58025

In these last years the theory of pseudodifferential operators has been reconsidered in the framework of the groupoids, see for example V. Nistor et al. [Pac. J. Math. 189, No. 1, 117–152 (1999; Zbl 0940.58014)] and the recent contribution of C. Debord et al. [Ann. Inst. Fourier 65, No. 4, 1799–1880 (2015; Zbl 1377.58025)]. In the present paper the authors propose a new approach, based on the kernel representation of the operators, under a suitable homogeneity assumption. As a particular case, they recapture classical pseudodifferential operators on compact manifolds and their properties. The presentation is addressed to a large audience, clarifying the connections with the other approaches.

MSC:

58J40 Pseudodifferential and Fourier integral operators on manifolds
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