4,851 research outputs found

    Regularity of some method of summation for double sequences

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    Some generalization of Toeplitz method of summation is introduced for double sequences and condition of regularity of it is obtained.<br /

    The Lr-Variational Integral

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    We define the Lr-variational integral and we prove that it is equivalent to the HKr-integral defined in 2004 by P. Musial and Y. Sagher in the Studia Mathematica paper The Lr-Henstock–Kurzweil integral. We prove also the continuity of Lr-variation function

    The arithmetic decomposition of central Cantor sets

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    Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor sets of Lebesgue measure zero. Under some mild condition this result can be strengthened by stating that the summands can be chosen to be Csregular if the initial set is of this class

    Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

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    Denjoy and P\mathcal P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform

    Inversion formulae for the integral transform on a locally compact zero-dimensional group

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    Generalized inversion formulae for multiplicative integral transform with a kernel defined by characters of a locally compact zero-dimensional abelian group are obtained using a Kurzweil-Henstock type integral
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