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A closed form for the symbol of the resolvent parametrix of an elliptic operator

Part of the Lecture Notes in Mathematics book series (LNM,volume 1285)

Keywords

  • Differential Operator
  • Vector Bundle
  • Covariant Derivative
  • Pseudodifferential Operator
  • Product Formula

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References

  1. F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators, Vol. 1, Plenum, New York, 1980; M. E. Taylor, Pseudodifferential Operators, Princeton Univ. Press, Princeton, 1981; H. Kumano-Go, Pseudo-Differential Operators, M.I.T. Press, Cambridge, Mass., 1982; B. E. Petersen, Introduction to the Fourier Transform and Pseudo-Differential Operators, Pitman, Boston, 1983; P. B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, Publish or Perish, Wilmington, 1984.

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  2. H. Widom, A complete symbolic calculus for pseudodifferential operators, Bull. Sci. Math. 104, 19–63 (1980); L. Drager, On the Intrinsic Symbol Calculus for Pseudo-Differential Operators on Manifolds, Ph.D. Dissertation, Brandeis University, 1978; J. Bokobza-Haggiag, Opérateurs pseudo-différentiels sur une variété différentiable, Ann. Inst. Fourier (Grenoble) 19, 125–177 (1969).

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  3. N. H. Barth and S. M. Christensen, Quantizing fourth order gravity theories: The functional integral, Phys. Rev. D 28, 1876–1893 (1983).

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  4. S. A. Fulling and G. Kennedy, The resolvent parametrix of the general elliptic linear differential operator: A closed form for the intrinsic symbol, in preparation.

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  5. S. A. Fulling and G. Kennedy, A closed form for the intrinsic symbol of the resolvent parametrix of an elliptic operator, in the proceedings of the First International Conference on the Physics of Phase Space (College Park, 1986), Springer Lecture Notes in Physics, to appear.

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© 1987 Springer-Verlag

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Fulling, S.A., Kennedy, G. (1987). A closed form for the symbol of the resolvent parametrix of an elliptic operator. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080588

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  • DOI: https://doi.org/10.1007/BFb0080588

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  • Print ISBN: 978-3-540-18479-9

  • Online ISBN: 978-3-540-47983-3

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