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Exceptional sets of projections, unions of k-planes and associated transforms

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Abstract

We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and apply it to a geometric problem.

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References

  1. M. Burak Erdoğan, A note on the Fourier transform of fractal measures, Mathematical Research Letters 11 (2004), 299–313.

    Article  MathSciNet  MATH  Google Scholar 

  2. K. Falconer, Hausdorff dimension and the exceptional set of projections, Mathematika 29 (1982), 109–115.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Kaufman, An exceptional set for Hausdorff dimension, Mathematika 16 (1969), 57–58.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Studies in Advanced Mathematics, Vol. 44, Cambridge University Press, Cambridge, 1995.

    Book  MATH  Google Scholar 

  5. D. Oberlin, Unions of hyperplanes, unions of spheres, and some related estimates, Illinois Journal of Mathematics 51 (2007), 1265–1274.

    MathSciNet  MATH  Google Scholar 

  6. Y. Peres and W. Schlag, Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions, Duke Mathematical Journal 102 (2000), 193–251.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Wolff, Decay of circular means of Fourier transforms of measures, International Mathematics Research Notices 10 (1999), 547–567.

    Article  Google Scholar 

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Correspondence to Daniel M. Oberlin.

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Oberlin, D.M. Exceptional sets of projections, unions of k-planes and associated transforms. Isr. J. Math. 202, 331–342 (2014). https://doi.org/10.1007/s11856-014-1040-4

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  • DOI: https://doi.org/10.1007/s11856-014-1040-4

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