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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:
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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.
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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).
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with Wilhelm Schlag,
On the Hardy-Littlewood majorant problem for random sets,
J. Funct. Anal., 256(4), (2009), 1189-1237.
pdf-file
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with Werner J. Ricker,
Optimal extension of the Hausdorff-Young inequality,
J. reine angew. Math., 620 (2008), 195-211. pdf-file
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with Werner J. Ricker,
Approximation of p-multiplier operators via Spectral projections.
Positivity 12, no. 1 (2008), 133-150,
link to Jour.
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Fourier Analysis und Kombinatorik.
Preprint-Reihe Mathematik 2008-1, Kath. Univ. Eichstaett-Ingolstadt.
pdf-file
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with Terence Tao,
Restriction and Kakeya phenomena for finite fields,
Duke Math. J. 121, no. 1 (2004), 35-74,
preprint.
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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.
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Salem sets and restriction properties of Fourier transforms,
Geom. and Func. Anal. 10, No.6, 1579-1587 (2000).
(pdf-file)
Note:
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with Werner J. Ricker,
Idempotent multipliers for Lp(R),
Arch. Math., 73(4), 1-5, (2000) .
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Some remarks on oscillatory integrals,
Research symposium on Geometric Analysis and Applications
at the ANU, Canberra, June 2000.
dvi-file
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Oscillatory integrals and curvature,
Proceedings of Workshops in Pure Mathematics,
Complex and Harmonic Analysis,
18(II):17-29, 1999.
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Bounds in Lebesgue spaces of oscillatory integrals,
Habilitation thesis, Universität Siegen, 1996.
djvu-file
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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.
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A note on the cone multiplier,
Proc. Amer. Math. Soc., 117(1):145-152, 1993.pdf-file
Note:
- 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.
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A restriction theorem for the Fourier transform,
Bull. Amer. Math. Soc., 25(1):31-36, 1991.
pdf-file
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Singuläre Integrale vom Bochner-Riesz Typ,
Dissertation, Universität Siegen, 1990.
pdf
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On radial weights for the spherical summation operator,
J. Funct. Anal.,91(1):174-181, 1990.
Note:
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Das Fouriersche Inversionsproblem unter Berücksichtigung der
Symmetrieeigenschaften der Fourier-Transformation,
Diploma thesis (in german), Siegen 1987.
djvu
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