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Journal of Fourier Analysis and Applications

, Volume 14, Issue 2, pp 301–325 | Cite as

Resolvent Estimates Related with a Class of Dispersive Equations

  • Hiroyuki ChiharaEmail author
Article

Abstract

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.

Keywords

Resolvent Dispersive equation Smoothing effect Limiting absorption principle 

Mathematics Subject Classification (2000)

47A10 35P25 47F05 

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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

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