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R E S E A R C H     I N T E R E S T S :
  • Fourier analysis
  • convergence of Fourier series, Bochner-Riesz means, Fourier Multipliers
  • oscillatory intergrals, restriction problems and their
    applications to pde's.
  • Functional analysis, spectral expansions

P U B L I C A T I O N S:
  • with Susumu Okada and Werner J. Ricker, Optimal extension of multiplier operators in L^p(G),
    Integral Equations and Operator Theory, 68, (2010), 573-599.

  • with Guillermo P.Curbera and Werner J. Ricker (eds), Vector Measures, Integration and Related Topics,
    Series: Operator Theory: Advances and Applications , Vol. 201 , Birkhaeuser , (2010).

  • with Wilhelm Schlag, On the Hardy-Littlewood majorant problem for random sets,
    J. Funct. Anal., 256(4), (2009), 1189-1237. pdf-file

  • with Werner J. Ricker, Optimal extension of the Hausdorff-Young inequality,
    J. reine angew. Math., 620 (2008), 195-211. pdf-file

  • with Werner J. Ricker, Approximation of p-multiplier operators via Spectral projections.
    Positivity 12, no. 1 (2008), 133-150, link to Jour.

  • Fourier Analysis und Kombinatorik.
    Preprint-Reihe Mathematik 2008-1, Kath. Univ. Eichstaett-Ingolstadt. pdf-file

  • with Terence Tao, Restriction and Kakeya phenomena for finite fields,
    Duke Math. J. 121, no. 1 (2004), 35-74, preprint.

  • with Werner J. Ricker, Fuglede's theorem, the bicommutant theorem and p-multiplier operators for the circle,
    Journal of Operator Theory, 49 (2003), no. 2, 295-310.

  • Salem sets and restriction properties of Fourier transforms,
    Geom. and Func. Anal. 10, No.6, 1579-1587 (2000). (pdf-file)


  • with Werner J. Ricker, Idempotent multipliers for Lp(R),
    Arch. Math., 73(4), 1-5, (2000) .

  • Some remarks on oscillatory integrals,
    Research symposium on Geometric Analysis and Applications at the ANU, Canberra, June 2000. dvi-file

  • Oscillatory integrals and curvature,
    Proceedings of Workshops in Pure Mathematics, Complex and Harmonic Analysis, 18(II):17-29, 1999.

  • Bounds in Lebesgue spaces of oscillatory integrals,
    Habilitation thesis, Universität Siegen, 1996. djvu-file

  • with Andreas Seeger and Chris Sogge, Local smoothing of Fourier integral operators and Carleson-Sjölin estimates,
    J. Amer. Math. Soc, 6(1):60-135, 1993.

  • A note on the cone multiplier,
    Proc. Amer. Math. Soc., 117(1):145-152, 1993.pdf-file

    • See the absolutly beautiful and well readable solution of Eli Stein's cone multiplier problem:
      by:Larry Guth, Hong Wang, Ruixiang Zhang
    • The developed technics go back to work of Andreas, Antony, Tom, Terry, Jean, Larry, S.Lee, J. Lee, Anna, Luis, Ciprian, Charles, Antonio, Ou, Hong, Chris, Jonathan, Willi and many more...

  • with Andreas Seeger and Chris Sogge, Wave front sets, local smoothing and Bourgain's circular maximal theorem,
    Ann. of Math., 136:207-218, 1992.

  • A restriction theorem for the Fourier transform,
    Bull. Amer. Math. Soc., 25(1):31-36, 1991. pdf-file

  • Singuläre Integrale vom Bochner-Riesz Typ,
    Dissertation, Universität Siegen, 1990. pdf

  • On radial weights for the spherical summation operator,
    J. Funct. Anal.,91(1):174-181, 1990.


  • Das Fouriersche Inversionsproblem unter Berücksichtigung der Symmetrieeigenschaften der Fourier-Transformation,
    Diploma thesis (in german), Siegen 1987. djvu