Asymptotics for Some Non-classical Conormal Distributions Whose Symbols Contain Negative Powers of log|ξ|

Research output: Research - peer-reviewArticle

Abstract

We examine distributions on (Formula presented.) whose Fourier coefficients are of the form (Formula presented.), and variants. These distributions are smooth except at (Formula presented.), and the nature of their singularities at (Formula presented.) turns out to be much more complex than those of their counterparts that involve positive powers of (Formula presented.). We also study related Fourier transforms. We move from one dimension to higher dimensions, where a wider variety of phenomena arise, and more subtle analytical techniques are called for.

LanguageEnglish (US)
Pages1-50
Number of pages50
JournalJournal of Fourier Analysis and Applications
DOIs
StateAccepted/In press - Mar 17 2017

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Fourier transforms
Fourier coefficients
One Dimension
Higher Dimensions
Fourier transform
Singularity

Keywords

  • Asymptotics
  • Conormal distribution
  • Fourier series
  • Fourier transform
  • Pseudodifferential operator
  • Symbols

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

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KW - Pseudodifferential operator

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