2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135373We 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.minor change, 20 pages, no figure, final versionAnalysis of PDEsClassical Analysis and ODEs47A10, 35P25, 47F05text