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- W2110292682 abstract "Here and in the following we shall suppose that this condition is satisfied. It is easy to show that F(x, r) is continuous. Since it can be shown (see [4]) that it is always pure, i.e. either absolutely continuous or purely singular, the question arises for which sequences r, F(x, r) enjoys the former or the latter property. Under the sole condition (I.3), very little is known to this date. There are some conditions (cf. [8]) on the speed of convergence of ,1.. rn which assure that F(x, r) is infinitely many times differentiable. These conditions are of the type n-z/nv 1/2 and all y > O. More recently Kahane and Salem (cf. [5]) have found a condition of arithmetical nature which, when applicable, assures not only that F(x, r) is absolutely continuous but that its Fourier transform is square integrable. Their result can be so described. Let" @default.
- W2110292682 created "2016-06-24" @default.
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- W2110292682 date "1962-01-01" @default.
- W2110292682 modified "2023-09-26" @default.
- W2110292682 title "Arithmetic properties of Bernoulli convolutions" @default.
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- W2110292682 doi "https://doi.org/10.1090/s0002-9947-1962-0137961-5" @default.
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