Abstract:
Singular measures in function theory are very understudied, in contrast to continuous and discrete measures. To fill this gap, the authors of this article have examined singular measures generated by a stochastic procedure using a homogeneous Markov chain. On the other hand, these measures can also be regarded as Fourier transforms of the probability distribution of the studied stochastic row. In [10] the basic properties of the discussed measures were described and proved, with the help of which it will be possible, firstly, to continue the study of singular measures on this example, and secondly, to try to apply the obtained mathematical results in statistics, information theory, signal processing.In this paper, the relationship between two singular measures is studied and recurrence relations linking them to each other are derived.The results obtained, besides their mathematical beauty, can be further used to study the asymptotic behaviour of these probability measures, to find their zeros, and to explore their properties as singular measures in more detail.
Keywords:singular measure, probability measure, stochastic row, Markov chain, Fourier transform.
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