The total symbol of a pseudo-differential operator
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- by Bent E. Petersen PDF
- Proc. Amer. Math. Soc. 30 (1971), 388-392 Request permission
Abstract:
This note presents a direct completely coordinate-free proof that the symbols of a pseudo-differential operator are differential operators whose coefficients are functions on the higher order cotangent bundles.References
- Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–517. MR 180740, DOI 10.1002/cpa.3160180307
- Richard S. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. MR 0198494
- Bent E. Petersen, On the calculus of symbols for pseudo-differential operators, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 169–173. MR 0267250
- Weishu Shih, On the symbol of a pseudo-differential operator, Bull. Amer. Math. Soc. 74 (1968), 657–659. MR 226661, DOI 10.1090/S0002-9904-1968-11981-0
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 388-392
- MSC: Primary 47.70; Secondary 35.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0288633-9
- MathSciNet review: 0288633