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Experimental Mathematics Volume 1, 1992 - Issue 4
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Original Articles

Numerical Experiments in Fourier Asymptotics of Cantor Measures and Wavelets

Prem Janardhan Susquehanna University, Selingrove, PA, 17870 E-mail: [email protected]
,
David Rosenblum Amherst College, P. O. Box 1647, Amherst, MA, 01002 E-mail: [email protected]
&
Robert S. Strichartz Mathematics Department, White Hall, Cornell University, Ithaca, NY, 14853 E-mail: [email protected]
Pages 249-273 | Published online: 03 Apr 2012

REFERENCES

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  • Daubechies , I. Ten Lectures on Wavelets . CBMS-NSF Regional Conference Series in Applied Mathematics 61 . Philadelphia : SIAM. . [Daubechies 1992]
  • Erdős , P. 1940 . “On the smoothness properties of a family of Bernoulli convolutions” . Amer. J. Math. , 62 : 180 – 186 . [Erdős 1940]
  • Furstenberg , H. and Kesten , H. 1960 . “Products of random matrices” . Ann. Math. Statist. , 31 : 457 – 469 . [Furstenberg and Kesten 1960]
  • Hutchinson , J. 1981 . “Fractals and self-similarity” . Indiana Univ. Math. J. , 30 : 713 – 747 . [Hutchinson 1981]
  • Koksma , J. F. 1935 . “Ein mengentheoretischer Satz über die Gleichverteilung modulo Eins” . Compositio Math. , : 250 – 258 . [Koksma 1935]
  • Lau , K.-S. 1992 . “Fractal measures and mean p- variations” . J. Funct. Anal. , 108 : 427 – 457 . [Lau]
  • Lau , K.-S. and Wang , J. “Mean quadratic variations and Fourier asymptotics of self-similar measures” [Lau and Wang], to appear in Monatsh. Math.
  • Salem , R. 1983 . Algebraic Numbers and Fourier Analysis Belmont , CA : Wadsworth. . [Salem 1983]
  • Strichartz , R. S. 1990 . “Self-similar measures and their Fourier transforms I” . Indiana Univ. Math. J. , 39 : 797 – 817 . [Strichartz 1990]
  • Strichartz , R. S. 1992 . “Self-similarity on nilpotent Lie groups” . Contemp. Math. , 140 : 123 – 157 . [Strichartz 1992a]
  • Strichartz , R. S. 1992 . “Self-similar measures and their Fourier transforms III” Cornell University. . [Strichartz 1992b], (preprint)
  • Strichartz , R. S. 1993 . “Self-similar measures and their Fourier transforms II” . Trans. Amer. Math. Soc. , [Strichartz 1993], to appear in
  • Wiener , N. and Wintner , A. 1939 . “On singular distributions” . J. Math. Phys. , 17 : 233 – 246 . [Wiener and Wintner 1939], Reprinted as pp. 687–700 in N. Wiener, Collected Works and Commentaries, vol. 2, MIT Press, Cambridge, MA, 1979

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