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Lower bounds for positive and negative parts of measures and the arrangement of singularities of their Laplace transforms

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Abstract

For a real measure with variation V(x) satisfying the estimate V(x) ≤ c 0 exp(Cx) and for the Laplace transform holomorphic in the disk {¦ -C¦ ≤ C} and having at least one pole of order m, we obtain lower bounds for the positive and negative parts of the measure V ± (x) > cx m, x > x 0. We establish lower bounds for V +- (x) on “short” intervals. Applications to number theory of the results obtained are considered.

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Authors and Affiliations

  1. Moscow State University, Russia

    A. Yu. Popov & A. P. Solodov

Authors
  1. A. Yu. Popov
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  2. A. P. Solodov
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Popov, A.Y., Solodov, A.P. Lower bounds for positive and negative parts of measures and the arrangement of singularities of their Laplace transforms. Math Notes 82, 75–87 (2007). https://doi.org/10.1134/S0001434607070103

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  • DOI: https://doi.org/10.1134/S0001434607070103

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