The normal symbol on Riemannian manifolds

New York Journal of Mathematics

Volumn 4, Issue , 1998, Pages 97-125

  Pflaum, Markus J ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Asymptotic expansions; Pseudodifferential operators on manifolds; Symbol calculus

Indexed keywords

EID: 0002318354     PISSN: 10769803     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. N. Berline, E. Getzler, and M. Vergne, Heat Kernels and Dirac Operators, Grundlehren der mathematischen Wissenschaften, no. 298, Springer-Verlag, Berlin, 1992.
2. A. Douglis and L. Nirenberg, Interior estimates for elliptic systems of partial differential equations, Comm. Pure Appl. Math. 8 (1955), 503-538.
3. J. J. Duistermaat, Fourier Integral Operators, Courant Institute of Math. Sci., New York, 1973.
4. Ezra Getzler, Pseudodifferential operators on supermanifolds and the Atiyah-Singer Index Theorem, Comm. Math. Phys. 92 (1983), 163-178.
5. Alain Grigis and Johannes Sjøstrand, Microlocal Analysis for Differential Operators, London Mathematical Society Lecture note series, no. 196, Cambridge University Press, Cambridge, 1994.
6. Lars Hörmander, The Analysis of Linear Partial Differential Operators I, Grundlehren, no. 256, Springer-Verlag, Berlin, 1983.
7. _, The Analysis of Linear Partial Differential Operators III, Grundlehren, no. 274, Springer-Verlag, Berlin, 1985.
8. Markus J. Pflaum, Local Analysis of Deformation Quantization, Ph.D. thesis, Fakultät für Mathematik der Ludwig-Maximilians- Universität, München, November 1995.
9. _, A deformation theoretical approach to Weyl quantization on Riemannian manifolds, Lett. Math. Physics (to appear).
10. Yuri Safarov, Functions of the Laplace-Beltrami operator, Journees "Equations aux derivees partielles", (Saint-Jean-de-Monts, 1996), Exp. No. XV, 8 pp., École Polytech., Palaiseau, 1996.
11. _, Pseudodifferential operators and linear connections, Proc. London Math. Soc. (3) (to appear).
12. M. A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, 1987.
13. Harold Widom, Families of pseudodifferential operators, Topics in Functional Analysis (I. Gohberg and M. Kac, eds.), Academic Press, New York, 1978, pp. 345-395.
14. _, A complete symbolic calculus for pseudodifferential operators, Bull. Sci. Math. (2) 104 (1980), 19-63.