Fourier Asymptotics of Statistically Self-Similar Measures

Journal of Fourier Analysis and Applications

Volumn 5, Issue 4, 1999, Pages 355-362

  Bluhm, Christian ^a  

^a UNIVERSITY OF GREIFSWALD   (Germany)

Author keywords

Fourier dimension; Random self similar measures; Salem sets

Indexed keywords

EID: 0033410265     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01259376     Document Type: Article

References (15)

1. Arbeiter, M. (1991). Random recursive construction of self-similar fractal measures. The noncompact case, Probab. Th. Rel. Fields, 88, 497-520.
2. Arbeiter, M. (1992). Construction of random fractal measures by branching processes, Stochastics and Stochastics Reports, 39, 195-212.
3. Arbeiter, M. and Patzschke, N. (1996). Random self-similar multifractals, Math. Nachr., 181, 5-42.
4. Bluhm, C. (1996). Zur Konstruktion von Salem-Mengen. Doctoral Thesis, University of Erlangen-Nürnberg.
5. Bluhm, C. (1996). Random recursive construction of Salem sets, Ark. Mat., 34, 51-63.
6. Falconer, K.J. (1986). Random fractals, Math. Proc. Cambridge Phil. Soc., 100, 559-582.
7. Graf, S. (1987). Statistically self-similar fractals, Probab. Th. Rel. Fields, 74, 357-392.
8. Graf, S., Mauldin, R.D., and Williams, S.C. (1988). The exact Hausdorff dimension in random recursive constructions, Memoirs Amer. Math. Soc., 381.
9. Kahane, J.-P. (1985). Some Random Series of Functions, 2nd ed., Cambridge University Press, Cambridge.
10. Kahane, J.-P. and Mandelbrot, B. (1965). Ensembles de multiplicité aléatoires, C. R. Acad. Sc. Paris, 261, 3931-3933.
11. Mattila, P. (1995). Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, Cambridge University Press, Cambridge.
12. Mauldin, R.D. and Williams, S.C. (1986). Random recursive constructions: asymptotic geometric and topological properties, Trans. Amer. Math. Soc., 295(1), 325-346.
13. Patzschke, N. and Zähle, U. (1990). Self-similar random measures. IV - The recursive construction model of Falconer, Graf, and Mauldin and Williams, Math. Nachr., 149, 285-302.
14. Salem, R. (1950). On singular monotonie functions whose spectrum has a given Hausdorff dimension, Ark. Mat., 1, 353-365.
15. Zygmund, A. (1968). Trigonometric series, Vol. I, II, Cambridge University Press, Cambridge.