Document Open Access Logo

Time-Frequency Analysis and PDE's

Author Anita Tabacco

PDF

File

Thumbnail PDF
PDF
DagSemProc.08492.10.pdf
  • Filesize: 165 kB
  • 4 pages

Document Identifiers

Subject Classification

Keywords
  • Fourier multipliers
  • modulation spaces
  • short-time Fourier transform

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We study the action on modulation spaces of Fourier multipliers with symbols
$e^{imu(xi)}$, for real-valued functions $mu$ having unbounded second
derivatives. We show that if $mu$ satisfies the usual symbol estimates of order
$alphageq2$, or if $mu$ is a positively homogeneous function of degree $alpha$,
the corresponding Fourier multiplier is bounded as an operator between the weighted modulation spaces $mathcal{M}^{p,q}_delta$ and $mathcal{M}^{p,q}$,
for every $1leq p,qleqinfty$ and $deltageq d(alpha-2)|frac{1}{p}-frac{1}{2}|$.
Here $delta$ represents the loss of derivatives. The above threshold is shown to
be sharp for {it all} homogeneous functions $mu$ whose Hessian matrix is
non-degenerate at some point.

Cite As Get BibTex

Anita Tabacco. Time-Frequency Analysis and PDE's. In Structured Decompositions and Efficient Algorithms. Dagstuhl Seminar Proceedings, Volume 8492, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/DagSemProc.08492.10

Author Details

Anita Tabacco
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact