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The total symbol of a pseudo-differential operator

Author: Bent E. Petersen
Journal: Proc. Amer. Math. Soc. 30 (1971), 388-392
MSC: Primary 47.70; Secondary 35.00
MathSciNet review: 0288633
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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.

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  • [1] L. Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501-517. MR 31 #4970. MR 0180740 (31:4970)
  • [2] R. S. Palais et al., Seminar on the Atiyah-Singer index theorem, Ann. of Math. Studies, no. 57, Princeton Univ. Press, Princeton, N. J., 1965. MR 33 #6649. MR 0198494 (33:6649)
  • [3] B. E. Petersen, On the calculus of symbols for pseudo-differential operators, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R. I., 1970, pp. 169-173. MR 0267250 (42:2152)
  • [4] W. Shih, On the symbol of a pseudo-differential operator, Bull. Amer. Math. Soc. 74 (1968), 657-659. MR 37 #2249. MR 0226661 (37:2249)

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Keywords: Pseudo-differential operators, symbol
Article copyright: © Copyright 1971 American Mathematical Society

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