Geodesic
Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem
Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 809-835
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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: Fejér and Bohman extremal problems
Mots-clés : Sturm-Liouville problem, Fourier transform, Turán, Gauss and Markov quadrature formulae. 
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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. Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 809-835. http://geodesic.mathdoc.fr/item/SM_2019_210_6_a2/

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