A groupoid approach to pseudodifferential calculi

References

[1] B. Ammann, R. Lauter and V. Nistor, Pseudodifferential operators on manifolds with a Lie structure at infinity, Ann. of Math. (2) 165 (2007), no. 3, 717–747. 10.4007/annals.2007.165.717Search in Google Scholar

[2] R. Beals and P. Greiner, Calculus on Heisenberg manifolds, Ann. of Math. Stud. 119, Princeton University Press, Princeton 1988. 10.1515/9781400882397Search in Google Scholar

[3] P. Carrillo Rouse, A Schwartz type algebra for the tangent groupoid, K-theory and noncommutative geometry, EMS Ser. Congr. Rep., European Mathematical Society, Zürich (2008), 181–199. 10.4171/060-1/7Search in Google Scholar

[4] W. Choi and R. Ponge, Privileged coordinates and tangent groupoid for Carnot manifolds, preprint (2015), http://arxiv.org/abs/1510.05851. Search in Google Scholar

[5] M. Christ, D. Geller, P. Głowacki and L. Polin, Pseudodifferential operators on groups with dilations, Duke Math. J. 68 (1992), no. 1, 31–65. 10.1215/S0012-7094-92-06802-5Search in Google Scholar

[6] A. Connes, Sur la théorie non commutative de l’intégration, Algèbres d’opérateurs (Les Plans-sur-Bex 1978), Lecture Notes in Math. 725, Springer, Berlin (1979), 19–143. 10.1007/BFb0062614Search in Google Scholar

[7] A. Connes, Noncommutative geometry, Academic Press, San Diego 1994. Search in Google Scholar

[8] T. E. Cummins, A pseudodifferential calculus associated to 3-step nilpotent groups, Comm. Partial Differential Equations 14 (1989), no. 1, 129–171. 10.1080/03605308908820593Search in Google Scholar

[9] S. Dave and S. Haller, Graded hypoellipticity of BGG sequences, preprint (2017), http://arxiv.org/abs/1705.01659. 10.1007/s10455-022-09870-0Search in Google Scholar

[10] C. Debord, J.-M. Lescure and F. Rochon, Pseudodifferential operators on manifolds with fibred corners, Ann. Inst. Fourier (Grenoble) 65 (2015), no. 4, 1799–1880. 10.5802/aif.2974Search in Google Scholar

[11] C. Debord and G. Skandalis, Adiabatic groupoid, crossed product by ℝ+∗ and pseudodifferential calculus, Adv. Math. 257 (2014), 66–91. 10.1016/j.aim.2014.02.012Search in Google Scholar

[12] C. Epstein and R. Melrose, The Heisenberg algebra, index theory and homology, unpublished book, http://www-math.mit.edu/~rbm/book.html. Search in Google Scholar

[13] L. Hörmander, The analysis of linear partial differential operators. III: Pseudodifferential operators, Grundlehren Math. Wiss. 274, Springer, Berlin 1985. Search in Google Scholar

[14] J.-M. Lescure, D. Manchon and S. Vassout, About the convolution of distributions on groupoids, J. Noncommut. Geom. 11 (2017), no. 2, 757–789. 10.4171/JNCG/11-2-10Search in Google Scholar

[15] K. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Math. Soc. Lecture Note Ser. 124, Cambridge University Press, Cambridge 1987. 10.1017/CBO9780511661839Search in Google Scholar

[16] A. Melin, Lie filtrations and pseudo-differential operators, preprint (1982). Search in Google Scholar

[17] R. B. Melrose, Transformation of boundary problems, Acta Math. 147 (1981), no. 3–4, 149–236. 10.1007/BF02392873Search in Google Scholar

[18] R. B. Melrose, The Atiyah–Patodi–Singer index theorem, Research Notes in Math. 4, A K Peters, Wellesley 1993. 10.1201/9781439864609Search in Google Scholar

[19] R. B. Melrose and P. Piazza, Analytic K-theory on manifolds with corners, Adv. Math. 92 (1992), no. 1, 1–26. 10.1016/0001-8708(92)90059-TSearch in Google Scholar

[20] I. Moerdijk and J. Mrčun, Introduction to foliations and Lie groupoids, Cambridge Stud. Adv. Math. 91, Cambridge University Press, Cambridge 2003. 10.1017/CBO9780511615450Search in Google Scholar

[21] B. Monthubert, Pseudodifferential calculus on manifolds with corners and groupoids, Proc. Amer. Math. Soc. 127 (1999), no. 10, 2871–2881. 10.1090/S0002-9939-99-04850-9Search in Google Scholar

[22] B. Monthubert and F. Pierrot, Indice analytique et groupoïdes de Lie, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 2, 193–198. 10.1016/S0764-4442(97)84598-3Search in Google Scholar

[23] A. Nagel and E. M. Stein, Lectures on pseudodifferential operators: Regularity theorems and applications to nonelliptic problems, Math. Notes 24, Princeton University Press, Princeton 1979. Search in Google Scholar

[24] V. Nistor, A. Weinstein and P. Xu, Pseudodifferential operators on differential groupoids, Pacific J. Math. 189 (1999), no. 1, 117–152. 10.2140/pjm.1999.189.117Search in Google Scholar

[25] R. Ponge, The tangent groupoid of a Heisenberg manifold, Pacific J. Math. 227 (2006), no. 1, 151–175. 10.2140/pjm.2006.227.151Search in Google Scholar

[26] R. S. Ponge, Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds, Mem. Amer. Math. Soc. 194 (2008), no. 906. 10.1090/memo/0906Search in Google Scholar

[27] A. R. H. S. Sadegh and N. Higson, Euler-like vector fields, deformation spaces and manifolds with filtered structure, preprint (2016), http://arXiv.org/abs/1611.05312. Search in Google Scholar

[28] M. Taylor, Noncommutative microlocal analysis. Part I (revised version), preprint, http://www.unc.edu/math/Faculty/met/NCMLMS.pdf. Search in Google Scholar

[29] F. Trèves, Introduction to pseudodifferential and Fourier integral operators. Vol. 1, Plenum Press, New York 1980. 10.1007/978-1-4684-8780-0Search in Google Scholar

[30] E. van Erp, The Atiyah–Singer index formula for subelliptic operators on contact manifolds, ProQuest LLC, Ann Arbor 2005; Ph.D. thesis, The Pennsylvania State University. Search in Google Scholar

[31] E. van Erp, The Atiyah–Singer index formula for subelliptic operators on contact manifolds. Part I, Ann. of Math. (2) 171 (2010), no. 3, 1647–1681. 10.4007/annals.2010.171.1647Search in Google Scholar

[32] E. van Erp and R. Yuncken, On the tangent groupoid of a filtered manifold, preprint (2016), http://arxiv.org/abs/arXiv:1611.01081. 10.1112/blms.12096Search in Google Scholar