Resolvent Estimates Near the Boundary of the Range of the Symbol

  • Johannes Sjöstrand
Part of the Pseudo-Differential Operators book series (PDO, volume 14)


In this chapter, which closely follows, we study bounds on the resolvent of a non-self-adjoint h-pseudodifferential operator P with (semi-classical) principal symbol p when h → 0, when the spectral parameter is in a neighborhood of certain points on the boundary of the range of p. In Chap.  6 we have already described a very precise result of W. Bordeaux Montrieux in dimension 1. Here we consider a more general situation; the dimension can be arbitrary and we allow for more degenerate behaviour. The results will not be quite as precise as in the one-dimensional case.


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Authors and Affiliations

  • Johannes Sjöstrand
    • 1
  1. 1.Université de Bourgogne Franche-ComtéDijonFrance

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