On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets

Arkiv for Matematik

Volumn 36, Issue 2, 1998, Pages 307-316

  Bluhm, Christian ^a  

^a UNIVERSITY OF GREIFSWALD   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038583203     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02384771     Document Type: Article

References (13)

1. BESICOVITCH, A. S., Sets of fractional dimensions (IV): on rational approximation to real numbers, J. London Math. Soc. 9 (1934), 126-131.
2. BLUHM, C., Zur Konstruktion von Salem-Mengen, Ph. D. Dissertation, Erlangen, 1996.
3. BLUHM, C., Random recursive construction of Salem sets, Ark. Mat. 34 (1996), 51-63.
4. DODSON, M. M., Geometric and probabilistic ideas in metric Diophantine approximation, Uspekhi Mat. Nauk 48:5 (1995), 77-106 (Russian). English transl.: Russian Math. Surveys 48:5 (1993), 73-102.
5. DODSON, M. M., Geometric and probabilistic ideas in metric Diophantine approximation, Uspekhi Mat. Nauk 48:5 (1995), 77-106 (Russian). English transl.: Russian Math. Surveys 48:5 (1993), 73-102.
6. GATESOUPE, M., Sur un théorème de R. Salem, Bull. Sci. Math. 91 (1967), 125-127.
7. HARDY, G. H. and WRIGHT, E. M., An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, Oxford, 1979.
8. JARNÍK, V., Zur metrischen Theorie der diophantischen Approximation, Prace Mat.-Fiz. 36 (1928/29), 91-106.
9. KAHANE, J.-P., Some Random Series of Functions, 2nd ed., Cambridge Univ. Press, Cambridge, 1985.
10. KAHANE, J.-P. and MANDELBROT, B., Ensembles de multiplicité aléatoires, C. R. Acad. Sci. Paris Sér. I Math. 261 (1965), 3931-3933.
11. KAUFMAN, R., On the theorem of Jarník and Besicovitch, Acta Arith. 39 (1981), 265-267.
12. MATTILA, P., Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, Cambridge Univ. Press, Cambridge, 1995.
13. SALEM, R., On singular monotonic functions whose spectrum has a given HausdorfT dimension, Ark. Mat. 1 (1950), 353-365.