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Multilinear Fourier multipliers related to time–frequency localization

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Identifiers
DOI: 10.1016/j.jmaa.2012.08.043
Keywords
  • Multilinear Fourier Multiplier
  • Bilinear Pseudodifferential Operator
  • Time–Frequency
  • Localization Operator
  • Bilinear Compact Operator
Disciplines
  • Mathematics

Abstract

Abstract We consider multilinear multipliers associated in a natural way with localization operators. Boundedness and compactness results are obtained. In particular, we get a geometric condition on a subset A⊂R2d which guarantees that, for a fixed synthesis window ψ∈L2(Rd), the family of localization operators Lφ,ψA obtained when the analysis window φ varies on the unit ball of L2(Rd) is a relatively compact set of compact operators.

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