Intrinsic microlocal analysis and inversion formulae for the heat equation on compact real-analytic riemannian manifolds
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 29 (1996) no. 6, p. 669-736
@article{ASENS_1996_4_29_6_669_0,
     author = {Leichtnam, \'Eric and Golse, Fran\c cois and Stenzel, Matthew},
     title = {Intrinsic microlocal analysis and inversion formulae for the heat equation on compact real-analytic riemannian manifolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 29},
     number = {6},
     year = {1996},
     pages = {669-736},
     doi = {10.24033/asens.1751},
     zbl = {0889.32037},
     mrnumber = {97h:58153},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1996_4_29_6_669_0}
}
Leichtnam, Éric; Golse, François; Stenzel, Matthew. Intrinsic microlocal analysis and inversion formulae for the heat equation on compact real-analytic riemannian manifolds. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 29 (1996) no. 6, pp. 669-736. doi : 10.24033/asens.1751. http://www.numdam.org/item/ASENS_1996_4_29_6_669_0/

[B-L-R] C. Bardos, G. Lebeau and J. Rauch, Scattering Frequencies and Gevrey 3 Singularities (Inv. Math., Vol. 90, 1987, pp. 77-114). | MR 89h:35252 | Zbl 0723.35058

[B-G-M] M. Berger, P. Gauduchon and E. Mazet, Le Spectre d'une Variété Riemannienne (Lecture Notes in Mathematics, 194, Springer Verlag). | MR 43 #8025 | Zbl 0223.53034

[BdM] L. Boutet De Monvel, Convergence dans le domaine complexe des séries de fonctions propres (C. R. Acad. Sc. Paris, T. 287, Series A, 1978, pp. 855-856). | MR 80i:58040 | Zbl 0392.35043

[Bo] A. Borel, Compact Clifford-Klein forms of symmetric spaces (Topology, Vol. 2, 1963, pp. 111-122). | MR 26 #3823 | Zbl 0116.38603

[B-W] F. Bruhat and H. Whitney, Quelques propriétés fondamentales des ensembles analytiques-réels (Commentarii Math. Helvet., Vol. 33, 1959, pp. 132-160). | MR 21 #889 | Zbl 0100.08101

[C-P] Chazarain-Piriou, Introduction à la Théorie des Équations aux Dérivées Partielles Linéaires, Gauthier-Villars. | Zbl 0446.35001

[C] A. Connes, Noncommutative Geometry (Academic Press, New York 1994). | MR 95j:46063 | Zbl 0818.46076

[D] J-M. Delort, FBI Transformation, Second Microlocalization and Semilinear Caustics, (Lecture Notes in Mathematics, 1522, Springer Verlag). | Zbl 0760.35004

[D-G] J. Duistermaat and V. Guillemin, The Spectrum of Positive Elliptic Operators and Periodic Bicharacteristics (Inv. Math., Vol. 29, 1975, pp. 39-79). | MR 53 #9307 | Zbl 0307.35071

[E-M] C. Epstein and R. Melrose, Shrinking tubes and the ∂-Neumann problem, preprint 1991.

[G] V. Guillemin, Toeplitz Operators in n-dimensions, Integral Equations and Operator Theory, Vol. 7, 1984, pp. 145-205. | MR 86i:58130 | Zbl 0561.47025

[G-S1] V. Guillemin and M. Stenzel, Grauert tubes and the homogeneous Monge-Ampère equation. I (J. Differential Geometry, Vol. 34, 1991, pp. 561-570). | MR 93e:32018 | Zbl 0746.32005

[G-S2] V. Guillemin and M. Stenzel, Grauert tubes and the homogeneous Monge-Ampère equation. II (J. Differential Geometry, Vol. 35, 1992, pp. 627-641). | MR 94e:32032 | Zbl 0789.32010

[He1] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, 2nd ed. (Academic Press, 1978). | Zbl 0451.53038

[He2] S. Helgason, Groups and Geometric Analysis (Academic Press, 1984). | MR 86c:22017 | Zbl 0543.58001

[Hz] P. Heinzner, Equivariant holomorphic extensions of real analytic manifolds, (Bull. Soc. Math. France, Vol. 121, 1993, pp. 445-463). | Numdam | MR 94i:32050 | Zbl 0794.32022

[Ho] G. Hochschild, The Structure of Lie Groups Holden-Day, 1965. | MR 34 #7696 | Zbl 0131.02702

[K] Y. Kannai, Off diagonal short time asymptotics for fundamental solutions of diffusion equations (Communication in P.D.E., Vol. 2, 1977, pp. 781-830). | MR 58 #29247 | Zbl 0381.35039

[L1] G. Lebeau, Contrôle analytique I : estimations a priori (Duke Math. J., Vol. 68, 1992, pp. 1-30). | MR 93i:93019 | Zbl 0780.93053

[L2] G. Lebeau, Deuxième microlocalisation sur les sous-variétés isotropes (Annales de l'Institut Fourier, Vol. 35, 1985, pp. 145-217). | Numdam | MR 87h:58205 | Zbl 0539.58038

[Le] E. Leichtnam, Le problème de Cauchy ramifié linéaire pour des données à singularités algébriques (Mémoire de la SMF n° 53, 1993). | Numdam | MR 94j:35003a | Zbl 0789.35009

[L-S] L. Lempert and R. Szöke, Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds (Math. Ann., Vol. 290, 1991, pp. 689-712). | MR 92m:32022 | Zbl 0752.32008

[Sj] Sjöstrand, Singularités analytiques microlocales (Astérisque 95, 1982). | MR 84m:58151 | Zbl 0524.35007

[W] J. Wolf, Spaces of Constant Curvature, 2nd ed. Publish or Perish 1972. | MR 49 #7957 | Zbl 0281.53034