Products of singular continuous measures
HTML articles powered by AMS MathViewer
- by Alan Maclean
- Proc. Amer. Math. Soc. 68 (1978), 85-89
- DOI: https://doi.org/10.1090/S0002-9939-1978-0493171-0
- PDF | Request permission
Abstract:
Let G be a compact Abelian group. It is shown that if the Fourier transform of $f \in A(G)$ satisfies certain lacunary conditions, then f may be factored as the convolution product of singular continuous measures.References
- Gavin Brown, Riesz products and generalized characters, Proc. London Math. Soc. (3) 30 (1975), 209–238. MR 372530, DOI 10.1112/plms/s3-30.2.209
- Gavin Brown and William Moran, On orthogonality of Riesz products, Proc. Cambridge Philos. Soc. 76 (1974), 173–181. MR 350319, DOI 10.1017/s0305004100048830
- Raouf Doss, Convolution of singular measures, Studia Math. 45 (1973), 111–117. (errata insert). MR 328474, DOI 10.4064/sm-45-2-111-117
- Colin C. Graham and Alan MacLean, A multiplier theorem for continuous measures, Studia Math. 66 (1979/80), no. 3, 213–225. MR 579728, DOI 10.4064/sm-66-3-213-225 E. Hewitt and K. A. Ross, Abstract harmonic analysis, Volumes I and II, Springer-Verlag, New York-Heidelberg-Berlin, 1963 and 1970.
- Edwin Hewitt and Herbert S. Zuckerman, Singular measures with absolutely continuous convolution squares, Proc. Cambridge Philos. Soc. 62 (1966), 399–420. MR 193435, DOI 10.1017/s0305004100039992
- Jorge M. López and Kenneth A. Ross, Sidon sets, Lecture Notes in Pure and Applied Mathematics, Vol. 13, Marcel Dekker, Inc., New York, 1975. MR 0440298
- Offer Padé, Sur le spectre d’une classe de produits de Riesz, C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A1453–A1455 (French). MR 318760
- D. L. Salinger and N. Th. Varopoulos, Convolutions of measures and sets of analyticity, Math. Scand. 25 (1969), 5–18. MR 264334, DOI 10.7146/math.scand.a-10935
- Antoni Zygmund, On lacunary trigonometric series, Trans. Amer. Math. Soc. 34 (1932), no. 3, 435–446. MR 1501647, DOI 10.1090/S0002-9947-1932-1501647-3
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 85-89
- MSC: Primary 43A25
- DOI: https://doi.org/10.1090/S0002-9939-1978-0493171-0
- MathSciNet review: 0493171