Skip to main content

Hausdorff dimension, lacunary series, and some problems on exceptional sets

  • 436 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 266)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. G. Eggleston, Sets of fractional dimensions in number theory, Proc. London Math. Soc. 54(2) (1951), 42–93.

    MathSciNet  MATH  Google Scholar 

  2. H. Helson and J. P. Kahane, A fourier method in Diophantine problems, J. D'Analyse Math. 15 (1965), 245–262.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. R. Kaufman, A random method for lacunary series, J. D'Analyse Math. 22 (1969), 171–175.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. R. Kaufman, Lacunary series and probability, Pacific J. Math. 36 (1971), 195–200.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. S. Takahashi, Tohôku Math. J. 22 (1970), 502–510.

    CrossRef  Google Scholar 

  6. A. Zygmund, Trigonometric Series, Cambridge 1959 and 1968.

    Google Scholar 

Supplementary References

  1. A. S. Besicovitch, Sets of fractional dimensions (IV): On rational approximation to real numbers, J. London Math. Soc. 9 1934, 126–131.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. P. Erdos and S. J. Taylor, On the set of points of convergence of a lacunary trigonometric series..., Proc. London Math. Soc. 7 (3) (1957), 598–615.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. P. Erdos and S. J. Taylor, The Hausdorff measure of the intersection of positive Lebesgue measure, Mathematika 10 1963, 1–9.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. R. Kaufman, Probability, Hausdorff dimension, and fractional distribution, Mathematika 17 1970, 57–62.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. R. Kaufman, A remark on Sidon sets; Hausdorff measure and Sidon sets. (To appear.)

    Google Scholar 

  6. V. Jarník, Über einen Satz von A. Khintchine II, Acta Arithmetica 2 (1937), 1–22.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Kaufman, R. (1972). Hausdorff dimension, lacunary series, and some problems on exceptional sets. In: Gulick, D., Lipsman, R.L. (eds) Conference on Harmonic Analysis. Lecture Notes in Mathematics, vol 266. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059644

Download citation

  • DOI: https://doi.org/10.1007/BFb0059644

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05856-4

  • Online ISBN: 978-3-540-37479-4

  • eBook Packages: Springer Book Archive