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On some generalizations of theorems by Landau and Pólya

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Abstract

If F(s), the Mellin transform ƒ(x) (real valued), satisfies certain regularity conditions and if its behaviour on the abscissa of convergence is known, then theorems of Landau and Pólya give information concerning sign changes of ƒ(x). In the present paper, corresponding conclusions are obtained when F(s) does not satisfy the regularity conditions of the theorems of Landau Pólya.

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Authors and Affiliations

  1. University of Pennsylvania, Philadelphia

    Emil Grosswald

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  1. Emil Grosswald
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Written with the support of the National Science Foundation through the grant GP-3137.

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Grosswald, E. On some generalizations of theorems by Landau and Pólya. Israel J. Math. 3, 211–220 (1965). https://doi.org/10.1007/BF03008399

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  • DOI: https://doi.org/10.1007/BF03008399

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