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Mat. Sb., 2019, Volume 210, Number 6, Pages 56–81 (Mi msb9057)  

This article is cited in 1 scientific paper (total in 1 paper)

Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem

D. V. Gorbachev, V. I. Ivanov

Tula State University, Tula, Russia

Abstract: The Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem on the Cartesian product of half-lines are solved under natural conditions on a weight function defined as a product of one-dimensional weight functions. Extremal functions are constructed. A multivariate Markov quadrature formula is proved based on the zeros of eigenfunctions of the Sturm-Liouville problem. This quadrature formula is shown to be sharp on entire multivariate functions of exponential type. A Paley-Wiener type theorem is proved for the multivariate Fourier transform. A weighted $L^2$-analogue of the Kotel'nikov-Nyquist-Whittaker-Shannon sampling theorem is put forward.
Bibliography: 42 titles.

Keywords: Sturm-Liouville problem, Fourier transform, Turán, Fejér and Bohman extremal problems, Gauss and Markov quadrature formulae.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00308-а
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00308-a).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9057

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English version:
Sbornik: Mathematics, 2019, 210:6, 809–835

Bibliographic databases:

UDC: 517.518.86
MSC: Primary 42B10; Secondary 41A55, 34B24
Received: 30.12.2017 and 18.11.2018

Citation: D. V. Gorbachev, V. I. Ivanov, “Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem”, Mat. Sb., 210:6 (2019), 56–81; Sb. Math., 210:6 (2019), 809–835

Citation in format AMSBIB
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\pages 56--81
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    This publication is cited in the following articles:
    1. D. V. Gorbachev, N. N. Dobrovolskii, “Ob ekstremalnykh zadachakh tipa Nikolskogo–Bernshteina i Turana dlya preobrazovaniya Danklya”, Chebyshevskii sb., 20:3 (2019), 394–400  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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