References
Abraham, R., Marsden, J.: Foundations of mechanics. 2nd ed. Reading: Benjamin Cummings 1978
Adams, M.R., Ratiu, T., Schmid, R.: A Lie group structure for Fourier integral operators. Math. Ann. (to appear)
Adler, M.: On a trace functional for formal pseudo-differential operators and the symplectic structure for the Korteweg-deVries type equations. Invent. Math.50, 219–248 (1979)
Bokobza-Haggiag, J.: Opérateurs pseudo-différentiels sur une variété différentiable. Ann. Inst. Fourier, Grenoble19, 125–177 (1969)
Duistermaat, J.J.: Fourier integral operators. Lecture Notes, Courant Institute of Mathematical Sciences, New York, 1973
Ebin, D.G.: The manifold of Riemannian metrics. Bull. Am. Math. Soc.74, 1002–1004 (1968)
Ebin, D.G., Marsden, J.: Group of diffeomorphisms and the motion of incompressible fluid. Ann. Math.92, 102–163 (1970)
Guillemin, V., Sternberg, S.: Geometric asymptotics, American Mathematical Society Survey, Vol. 14. AMS, Providence, 1977
Hamilton, R.: The inverse function theorem of Nash and Moser. Bull. Am. Math. Soc.7, 65–222 (1982)
Hörmander, L.: Fourier integral operators. I. Acta Math.127, 79–183 (1971)
Iacob, A., Sternberg, S.: Coadjoint structures, solitons, and integrability. Lect. Notes Phys. 120. Berlin, Heidelberg, New York: Springer 1980
Kostant, B.: The solution to a generalized Toda lattice and representation theory. Adv. Math.34, 195–338 (1979)
Marsden, J., Well-posedness of equations of nonhomogeneous perfect fluid. Commun. Partial Differ Equations1, 215–230 (1976)
Marsden, J., Ebin, G.D., Fischer, A.: Diffeomorphism groups, hydrodynamics and relativity. In: Proc. 13th Biennial Seminar of Canadian Math. Congress, J.R. Vanstone (ed.), pp. 135–279. Montreal 1972
Omori, H.: Infinite dimensional Lie transformation groups. Lect. Notes Math. 427. Berlin, Heidelberg, New York: Springer 1974
Palais, R.: Foundations of global nonlinear analysis. Reading: Addison-Wesley 1968
Ratiu, T., Schmid, R.: The differentiable structure of three remarkable diffeomorphism groups. Math. Z.177, 81–100 (1981)
Symes, W.: Systems of Toda type, inverse spectral problems and representation theory. Invent. Math.59, 13–51 (1980)
Symes, W.: Hamiltonian group actions and integrable systems. Physica D1, 339–374 (1980)
Taylor, M.: Pseudodifferential operators. Princeton: Princeton University Press 1981
Trèves, F.: Introduction to pseudodifferential and Fourier integral operators. I, II. New York: Plenum Press 1980
Weinstein, A.: Lectures on symplectic manifolds. CBMS. Conference Series, Vol. 29. American Mathematical Society, Providence, 1977
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Research partially supported by: a NSF postdoctoral fellowship MCS 82-11332 b NSF postdoctoral fellowship MCS 83-11674 c NSF grants MCS 8301124 and MCS 8120790
This work was done while at the University of California, Berkeley, CA
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Adams, M., Ratiu, T. & Schmid, R. A Lie group structure for pseudodifferential operators. Math. Ann. 273, 529–551 (1986). https://doi.org/10.1007/BF01472130
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DOI: https://doi.org/10.1007/BF01472130