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Turán’s and Fejér’s Extremal Problems for Jacobi Transform

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Abstract

We give the solution of the Turán extremal problem for compact supported functions on the half-line with nonnegative Jacobi transform and the dual Fejér extremal problem for even nonnegative entire functions of exponential type that are Jacobi transforms. We prove the uniqueness of the extremal functions. The Markov quadrature formula on the half-line at zeros of the modified Jacobi function is used for the proof of these results.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Tula State University, 300012, Tula, Russia

    D. V. Gorbachev & V. I. Ivanov

Authors
  1. D. V. Gorbachev
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  2. V. I. Ivanov
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Correspondence to V. I. Ivanov.

Additional information

This work was supported by the Russian Foundation for Basic Research under grant 16-01-00308.

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Gorbachev, D.V., Ivanov, V.I. Turán’s and Fejér’s Extremal Problems for Jacobi Transform. Anal Math 44, 419–432 (2018). https://doi.org/10.1007/s10476-018-0304-z

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  • DOI: https://doi.org/10.1007/s10476-018-0304-z

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