Blowing up the corner where the semiclassical parameter meets the cotangent fiber identifies the semiclassical and standard pseudodifferential algebras and yields resolvent estimates for elliptic pseudodifferential spectral families.
Melrose, Spectral and scattering theory for the Laplacian on asymptotically Eu- clidian spaces, Spectral and scattering theory (Sanda, 1992), Lecture Notes in Pure and Appl
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On the relationship between the semiclassical and standard pseudodifferential algebras
Blowing up the corner where the semiclassical parameter meets the cotangent fiber identifies the semiclassical and standard pseudodifferential algebras and yields resolvent estimates for elliptic pseudodifferential spectral families.