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Superadditivity of the Levinson functional and applications

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Abstract

We study the Levinson functional, constructed as a difference between the right-hand side and the left-hand side of the Levinson inequality. We show that it possesses the properties of superadditivity and monotonicity. As a consequence, we obtain mutual bounds for this functional, expressed via the non-weighted functional of the same type. In this way, a refinement and a converse of the Levinson inequality in a difference form is obtained.

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Acknowledgments

The research of the authors has been fully supported by Croatian Science Foundation under the project 5435.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000, Zagreb, Croatia

    Mario Krnić

  2. Faculty of Civil Engineering and Architecture, University of Split, Matice hrvatske 15, 21000, Split, Croatia

    Neda Lovričević

  3. Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000, Zagreb, Croatia

    Josip Pečarić

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  1. Mario Krnić
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  2. Neda Lovričević
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  3. Josip Pečarić
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Correspondence to Mario Krnić.

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Krnić, M., Lovričević, N. & Pečarić, J. Superadditivity of the Levinson functional and applications. Period Math Hung 71, 166–178 (2015). https://doi.org/10.1007/s10998-015-0090-3

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