Dubnov, Vladimir L.; Maslov, Victor P.; Nazaikinskii, Vladimir E. The complex Lagrangian germ and the canonical operator. (English) Zbl 0920.58051 Russ. J. Math. Phys. 3, No. 2, 141-190 (1995); errata ibid. 4, No. 2, 271 (1996). From the authors’ abstract: “We give a manifestly invariant definition of the Lagrangian complex germ with the minimal degree of accuracy required to define the canonical operator. The equivalence with the traditional definition is proved, and the canonical operator is constructed in new terms. A new form of the quantization condition is given, in which the volume form is assumed to be defined on the universal covering of the Lagrangian manifold rather than on the manifold itself. This allows one to solve a wider class of eigenvalue problems”. Reviewer: W.M.Oliva (Lisboa) Cited in 2 Documents MSC: 58J37 Perturbations of PDEs on manifolds; asymptotics 35Q58 Other completely integrable PDE (MSC2000) 58J40 Pseudodifferential and Fourier integral operators on manifolds Keywords:Lagrangian complex germ; canonical operator PDFBibTeX XMLCite \textit{V. L. Dubnov} et al., Russ. J. Math. Phys. 3, No. 2, 1 (1995; Zbl 0920.58051) Full Text: arXiv