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Besicovitch meets Wiener—Fourier expansions and fractal measures
Author:
Robert S. Strichartz
Journal:
Bull. Amer. Math. Soc. 20 (1989), 55-59
MSC (1985):
Primary 28A75, 42B10; Secondary 42A75, 42B25, 46E35
MathSciNet review:
948764
Full-text PDF
References |
Similar Articles |
Additional Information
-
S.
Agmon and L.
Hörmander, Asymptotic properties of solutions of differential
equations with simple characteristics, J. Analyse Math.
30 (1976), 1–38. MR 0466902
(57 #6776)
-
[B1] A. S. Besicovitch, A general form of the covering principle and relative differentiation of additive functions. I, II, and Corrections, Proc. Cambridge Philos. Soc. 41 (1945), 103-110; 42 (1946), 1-10; 43 (1947), 590.
-
A.
S. Besicovitch, Almost periodic functions, Dover Publications
Inc., New York, 1955. MR 0068029
(16,817a)
-
K.
J. Falconer, The geometry of fractal sets, Cambridge Tracts in
Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. MR 867284
(88d:28001)
-
Miguel
de Guzmán, Real variable methods in Fourier analysis,
North-Holland Mathematics Studies, vol. 46, North-Holland Publishing
Co., Amsterdam, 1981. Notas de Matemática [Mathematical Notes], 75.
MR 596037
(83j:42019)
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Elias
M. Stein, Singular integrals and differentiability properties of
functions, Princeton Mathematical Series, No. 30, Princeton University
Press, Princeton, N.J., 1970. MR 0290095
(44 #7280)
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Robert
S. Strichartz, Harmonic analysis as spectral theory of
Laplacians, J. Funct. Anal. 87 (1989), no. 1,
51–148. MR
1025883 (91c:43015), http://dx.doi.org/10.1016/0022-1236(89)90004-9
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Robert
S. Strichartz, Fourier asymptotics of fractal measures, J.
Funct. Anal. 89 (1990), no. 1, 154–187. MR 1040961
(91m:42015), http://dx.doi.org/10.1016/0022-1236(90)90009-A
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Norbert
Wiener, The Fourier integral and certain of its applications,
dover Publications Inc., New York, 1959. MR 0100201
(20 #6634)
- [AH] S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, J. d'Analyse Math. 30 (1976), 1-38. MR 466902
- [B1] A. S. Besicovitch, A general form of the covering principle and relative differentiation of additive functions. I, II, and Corrections, Proc. Cambridge Philos. Soc. 41 (1945), 103-110; 42 (1946), 1-10; 43 (1947), 590.
- [B2] A. S. Besicovitch, Almost periodic functions, Dover, New York, 1954. MR 68029
- [F] K. J. Falconer, The geometry of fractal sets, Cambridge Univ. Press, 1985. MR 867284
- [G] M. de Guzman, Real variable methods in Fourier analysis, North-Holland, Amsterdam, 1981. MR 596037
- [S] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970. MR 290095
- [Str1] R. S. Strichartz, Harmonic analysis as spectral theory of Laplacians, J. Funct. Anal. (to appear). MR 1025883
- [Str2] R. S. Strichartz, Fourier asymptotics of fractal measures, preprint. MR 1040961
- [W] N. Wiener, The Fourier integral and certain of its applications, Dover, New York, 1933. MR 100201
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1989-15696-6
PII:
S 0273-0979(1989)15696-6
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