Given a Markov chain (not necessarily stationary or homogeneous) with finite state space and an initial distribution, we can construct a measure ~ on the unit interval [0,1]. In this work we examine the equality (up to a constant) of the Hausdorff dimension of/z and of a suitably defined entropy for the Markovian process. The results are applied to the so-called Rademacher-Riesz Products. 1991 Mathematics Subject Classification: 28A78, 42A55, 60G10.
ABSTRACT. We deal with the maximum Gibbs ripple of the sampling wavelet series of a discontinuous .function f at a point t ~ R, .for all possible values o.['a satisfying f (t) = ee.f (t -0) + (1 -cO.f (t + 0). For the Shannon wavelet series, we make a complete description of all ripples, .for any ot in [0,1]. We show that Meyer sampling series exhibit Gibbs Phenomenon.lor ce < 0.12495 and ct > 0.306853. We also give Meyer sampling formulas with maximum overshoots shorter than Shannon's for several et in [0,1].
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