Toric Resolution of Singularities in a Certain Class of $C^{infty}$ Functions and Asymptotic Analysis of Oscillatory Integrals

Journal of Mathematical Sciences

Nose, Toshihiro¹  Kamimoto, Joe¹ 

关键词: Oscillatory integrals;    oscillation index and its multiplicity;    local zeta function;    toric resolution;    the classes $hat{mathcal E}[P](U)$ and $hat{mathcal E}(U)$;    asymptotic expansion;    Newton polyhedra.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

InaseminalworkofA.N.Varchenko,thebehavioratinfinityofoscillatoryintegralswithrealanalyticphaseispreciselyinvestigatedbyusingthetheoryoftoricvarietiesbasedonthegeometryoftheNewtonpolyhedronofthephase.Thepurposeofthispaperistogeneralizehisresultstothecasethatthephaseiscontainedinacertainclassof$C^{infty}$functions.Thekeyinouranalysisisatoricresolutionofsingularitiesintheaboveclassof$C^{infty}$functions.Thepropertiesofpolesoflocalzetafunctions,whicharecloselyrelatedtothebehaviorofoscillatoryintegrals,arealsostudiedundertheassociatedsituation.

【 授权许可】

Unknown