Abstract:
We obtain a result concerning the basis property
in a weighted space on an interval (−a,a)
for a system of exponentials generated by the zeros
of the Fourier transform of a function with singularities
at the ends of the support interval (−a,a).
For an arbitrary Δ∈C we find a criterion
for the basis property of the system
(ei(n+Δsignn)t)n∈Z
in a weighted space on the interval (−π,π) and the systems
of sines (sin((n+Δ)t))n∈N and cosines
1∪(cos((n+Δ)t))n∈N in a weighted
space on the interval (0,π). The weight is everywhere
a finite product of polynomial functions.
\Bibitem{Puk11}
\by S.~S.~Pukhov
\paper Bases of exponentials, sines and cosines in weighted spaces on a~finite interval
\jour Izv. Math.
\yr 2011
\vol 75
\issue 2
\pages 413--443
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\crossref{https://doi.org/10.1070/IM2011v075n02ABEH002539}
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Linking options:
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This publication is cited in the following 7 articles:
M. I. Ismailov, I. F. Aliyarova, “On the basis property of the system of exponentials and trigonometric systems of sine and cosine functions in weighted grand Lebesgue spaces”, Moscow University Mathematics Bulletin, 79:2 (2024), 85–97
Yu. A. Kriksin, V. F. Tishkin, “On an approximation by band-limited functions”, Dokl. Math., 110:3 (2024), 500–505
Gasymov T.B., Akhtyamov A.M., Ahmedzade N.R., “On the Basicity of Eigenfunctions of a Second-Order Differential Operator With a Discontinuity Point in Weighted Lebesgue Spaces”, Proc. Inst. Math. Mech., 46:1 (2020), 32–44
V. R. Fatalov, “Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes:
exact asymptotics for Lp-functionals”, Izv. Math., 82:2 (2018), 377–406
Shukurov A.Sh., “On Basicity of the Degenerate Trigonometric System With Excess”, Acta Comment. Univ. Tartu. Math., 21:2 (2017), 249–257
S. S. Pukhov, “Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier–Stieltjes Transform”, Math. Notes, 95:6 (2014), 820–832
V. R. Fatalov, “Gaussian Ornstein–Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for Lp-functionals, 0<p<∞”, Problems Inform. Transmission, 50:4 (2014), 371–389