Geodesic
Tur\'an, Fej\'er 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

Voir la notice de l'article provenant de la source Math-Net.Ru

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: Turán, Fejér and Bohman extremal problems
Mots-clés : Sturm-Liouville problem, Fourier transform, Gauss and Markov quadrature formulae. 
@article{SM_2019_210_6_a2,
     author = {D. V. Gorbachev and V. I. Ivanov},
     title = {Tur\'an, {Fej\'er} and {Bohman} extremal problems for the multivariate {Fourier} transform in terms of the eigenfunctions of {a~Sturm-Liouville} problem},
     journal = {Sbornik. Mathematics},
     pages = {809--835},
     publisher = {mathdoc},
     volume = {210},
     number = {6},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_6_a2/}
}
TY  - JOUR
AU  - D. V. Gorbachev
AU  - V. I. Ivanov
TI  - Tur\'an, Fej\'er and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a~Sturm-Liouville problem
JO  - Sbornik. Mathematics
PY  - 2019
SP  - 809
EP  - 835
VL  - 210
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2019_210_6_a2/
LA  - en
ID  - SM_2019_210_6_a2
ER  - 
%0 Journal Article
%A D. V. Gorbachev
%A V. I. Ivanov
%T Tur\'an, Fej\'er and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a~Sturm-Liouville problem
%J Sbornik. Mathematics
%D 2019
%P 809-835
%V 210
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2019_210_6_a2/
%G en
%F SM_2019_210_6_a2
D. V. Gorbachev; V. I. Ivanov. Tur\'an, Fej\'er 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/