Resolvent estimates related with a class of dispersive equations

2007/04/03 by Hiroyuki Chihara, Chihara, Hiroyuki
Mathematics · #35P25 #47A10 #47F05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #advanced mathematical theories #math.AP #math.CA #msc:35P25 #msc:47A10 #msc:47F05

paper · pdf · doi:10.48550/arxiv.0704.0347

minor change, 20 pages, no figure, final version

openalex publication_date 2007/04/03 · arxiv created 2007/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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