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An intrinsic characterisation of polyhomogeneous Lagrangian distributions
Author(s):
M.
S.
Joshi
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1537-1543.
MSC (1991):
Primary 58G15
MathSciNet review:
1371128
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Abstract:
The purpose of this paper is to present a method of characterising polyhomogeneous Lagrangian distributions via testing by pseudo-differential operators. The concept of a radial operator for a Lagrangian submanifold is introduced, and polyhomogeneous Lagrangian distributions are shown to be the only Lagrangian distributions which are eigenfunctions at the top order for these operators.
References:
- 1.
- J.J. Duistermaat and L. Hörmander, Fourier Integral Operators II. Acta Mathematicae 128 (1972), 183-269. MR 52:9300
- 2.
- L. Hörmander, Fourier Integral Operators I, Acta Mathematicae 127 (1971), 79-183. MR 52:9299
- 3.
- L. Hörmander, Analysis of Linear Partial Differential Operators, Vol. 1 to 4, Springer Verlag, Berlin, 1983, 1985. MR 85g:35002a; MR 85g:35002b; MR 87d:35002a; MR 87d:35002b
- 4.
- M.S. Joshi, A Precise Calculus of Paired Lagrangian Distributions, M.I.T. thesis, 1994.
- 5.
- M.S. Joshi, A Symbolic Contruction of the Forward Fundamental Solution of the Wave Operator, preprint
- 6.
- R.B. Melrose, Differential Analysis on Manifolds with Corners, forthcoming.
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Additional Information:
M.
S.
Joshi
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England, United Kingdom
Email:
joshi@pmms.cam.ac.uk
DOI:
10.1090/S0002-9939-97-03737-4
PII:
S 0002-9939(97)03737-4
Keywords:
Lagrangian,
polyhomogeneity,
partial differential equations
Received by editor(s):
September 20, 1995
Received by editor(s) in revised form:
November 14, 1995
Additional Notes:
This research forms part of my thesis research carried out at the Massachusetts Institute of Technology under the supervision of R.B. Melrose, and I would like to thank him for his guidance and advice.
Communicated by:
Jeffrey B. Rauch
Copyright of article:
Copyright
1997,
American Mathematical Society
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