Time-Frequency Analysis and PDE's

Author Anita Tabacco

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Anita Tabacco

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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)


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


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