Zobrazeno 1 - 5
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pro vyhledávání: '"Minabutdinov, Aleksei"'
Autor:
Minabutdinov, Aleksei
Let $s(n)$ denote the number of "$1$"s in the dyadic representation of a positive integer $n$ and sequence $S(n) = s(1)+s(2)+\dots+s(n-1)$. The Trollope-Delange formula is a classic result that represents the sequence $S$ in terms of the Takagi funct
Externí odkaz:
http://arxiv.org/abs/2407.15201
Autor:
Minabutdinov, Aleksei
We study limiting curves resulting from deviations in partial sums in the ergodic theorem for the dyadic odometer and non-cylindric functions. In particular, we generalize the Trollope-Delange formula for the case of the weighted sum-of-binary-digits
Externí odkaz:
http://arxiv.org/abs/1801.03120
Autor:
Minabutdinov, Aleksei
We prove the existence and describe limiting curves resulting from deviations in partial sums in the ergodic theorem for cylindrical functions and polynomial (self-similar) adic systems. For a general ergodic measure-preserving transformation and a s
Externí odkaz:
http://arxiv.org/abs/1701.07617
Autor:
Minabutdinov, Aleksei
The paper extends the classical result on the convergence of the Krawtchouk polynomials to the Hermite polynomials. We provide the uniform asymptotic expansion in terms of the Hermite polynomials. We explicitly obtain expressions for a few initial te
Externí odkaz:
http://arxiv.org/abs/1508.07421
Publikováno v:
Journal of Mathematical Sciences. 216:94-119
The paper generalizes results by E. Janvresse, T. de la Rue, and Y. Velenik and results by the second author on the fluctuations in the ergodic sums for the Pascal adic transformation in the case of an arbitrary ergodic invariant measure and arbitrar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::49d0a1b21ffba5ba190824c287e1eb2e
https://doi.org/10.1007/s10958-016-2890-2
https://doi.org/10.1007/s10958-016-2890-2
