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URN: urn:nbn:de:0030-drops-18792
URL: http://drops.dagstuhl.de/opus/volltexte/2009/1879/
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Tabacco, Anita

Time-Frequency Analysis and PDE's

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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.

BibTeX - Entry

@InProceedings{tabacco:DSP:2009:1879,
  author =	{Anita Tabacco},
  title =	{Time-Frequency Analysis and PDE's},
  booktitle =	{Structured Decompositions and Efficient Algorithms},
  year =	{2009},
  editor =	{Stephan Dahlke and Ingrid Daubechies and Michal Elad and Gitta Kutyniok and Gerd Teschke},
  number =	{08492},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1879},
  annote =	{Keywords: Fourier multipliers, modulation spaces, short-time Fourier   transform}
}

Keywords: Fourier multipliers, modulation spaces, short-time Fourier transform
Seminar: 08492 - Structured Decompositions and Efficient Algorithms
Issue Date: 2009
Date of publication: 24.02.2009


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