Fractals and distributions on the $N$-torus
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- by Victor L. Shapiro
- Proc. Amer. Math. Soc. 131 (2003), 3431-3440
- DOI: https://doi.org/10.1090/S0002-9939-03-06929-6
- Published electronically: February 6, 2003
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Abstract:
This paper establishes non-Cartesian product sets, called fractal carpets and fractal foam, as sets of uniqueness for a class of trigonometric series.References
- J. M. Ash and G. Wang, Sets of uniqueness for spherically convergent multiple trigonometric series, preprint, 1999, 20 pages.
- L. Bers, F. John, and M. Schechter, Partial Differential Equations, Interscience Publishers, New York, 1964.
- Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301, Hermann, Paris, 1963 (French). MR 0160065
- Benoit B. Mandelbrot, The fractal geometry of nature, Schriftenreihe für den Referenten. [Series for the Referee], W. H. Freeman and Co., San Francisco, Calif., 1982. MR 665254
- Raphaël Salem, Algebraic numbers and Fourier analysis, D. C. Heath and Company, Boston, Mass., 1963. MR 0157941
- Victor L. Shapiro, Algebraic integers and distributions on the $N$-torus, J. Functional Analysis 13 (1973), 138–153. MR 0348392, DOI 10.1016/0022-1236(73)90041-4
- Victor L. Shapiro, Sets of uniqueness on the $2$-torus, Trans. Amer. Math. Soc. 165 (1972), 127–147. MR 308684, DOI 10.1090/S0002-9947-1972-0308684-0
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Bibliographic Information
- Victor L. Shapiro
- Affiliation: Department of Mathematics, University of California, Riverside, California 92521-0135
- Email: shapiro@math.ucr.edu
- Received by editor(s): July 3, 2001
- Received by editor(s) in revised form: May 25, 2002
- Published electronically: February 6, 2003
- Communicated by: Andreas Seeger
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3431-3440
- MSC (2000): Primary 42B35, 46F99; Secondary 42B05, 05A18
- DOI: https://doi.org/10.1090/S0002-9939-03-06929-6
- MathSciNet review: 1990632