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Fractals and distributions on the  -torus
Author(s):
Victor
L.
Shapiro
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3431-3440.
MSC (2000):
Primary 42B35, 46F99;
Secondary 42B05, 05A18
Posted:
February 6, 2003
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Additional information
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:
-
- [AW]
- J. M. Ash and G. Wang, Sets of uniqueness for spherically convergent multiple trigonometric series, preprint, 1999, 20 pages.
- [BJS]
- L. Bers, F. John, and M. Schechter, Partial Differential Equations, Interscience Publishers, New York, 1964.
- [KS]
- J. Kahane and R. Salem, Ensembles Parfait et Series Trigonométriques, Hermann, Paris, 1963. MR 28:3279
- [M]
- B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, New York, 1982. MR 84h:00021
- [Sa]
- R. Salem, Algebraic Numbers and Fourier Analysis, Heath, Boston, 1963. MR 28:1169
- [Sh1]
- V. L. Shapiro, Algebraic integers and distributions on the N-torus, J. Functional Analysis 13 (1973), pp. 138-153. MR 50:890
- [Sh2]
- V. L. Shapiro, Sets of uniqueness on the 2-torus, Trans. Amer. Soc. 165 (1972), pp. 127-147. MR 46:7798
- [Z1]
- A. Zygmund, Trigonometric Series, 2nd ed. Vol. I, Cambridge Univ. Press, New York, 1959. MR 21:6498
- [Z2]
- A. Zygmund, Trigonometric Series, 2nd ed. Vol. II, Cambridge Univ. Press, New York, 1959. MR 21:6498
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Additional Information:
Victor
L.
Shapiro
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521-0135
Email:
shapiro@math.ucr.edu
DOI:
10.1090/S0002-9939-03-06929-6
PII:
S 0002-9939(03)06929-6
Keywords:
Fractal,
carpet,
distribution,
$N$-torus
Received by editor(s):
July 3, 2001
Received by editor(s) in revised form:
May 25, 2002
Posted:
February 6, 2003
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2003,
American Mathematical Society
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