Resolvent estimates related with a class of dispersive equations

Details Resolvent estimates related with a class of dispersive equations Resolvent estimates related with a class of dispersive equations

2007-04-03

arxiv.org/abs/0704.0347v2

Mathematics

Analysis of PDEs

minor change, 20 pages, no figure, final version

Scientific paper

We present a simple proof of the resolvent estimates of elliptic Fourier multipliers on the Euclidean space, and apply them to the analysis of time-global and spatially-local smoothing estimates of a class of dispersive equations. For this purpose we study in detail the properties of the restriction of Fourier transform on the unit cotangent sphere associated with the symbols of multipliers.

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