Abstract:
We consider systems of exponentials that are orthogonal to measures $d\sigma$ of a special form on $(-a,a)$. Under certain conditions on the summation method, these systems form summation bases $L^p(-a,a)$ and in $C_0$ (the subspace of $C[-a,a]$ orthogonal
to $d\sigma$). With respect to these systems, Lipschitzian functions in $C_0$ are expanded into non-harmonic Fourier series that converge uniformly on $[-a,a]$.
\Bibitem{Sed00}
\by A.~M.~Sedletskii
\paper On the summability and convergence of non-harmonic Fourier series
\jour Izv. Math.
\yr 2000
\vol 64
\issue 3
\pages 583--600
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\crossref{https://doi.org/10.1070/im2000v064n03ABEH000292}
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This publication is cited in the following 7 articles:
Gilbert Kerr, Nehemiah Lopez, Gilberto González-Parra, “Analytical Solutions of Systems of Linear Delay Differential Equations by the Laplace Transform: Featuring Limit Cycles”, MCA, 29:1 (2024), 11
Michelle Sherman, Gilbert Kerr, Gilberto González-Parra, “Analytical solutions of linear delay-differential equations with Dirac delta function inputs using the Laplace transform”, Comp. Appl. Math., 42:6 (2023)
Anton Baranov, Yurii Belov, Aleksei Kulikov, “Spectral synthesis for exponentials and logarithmic length”, Isr. J. Math., 250:1 (2022), 403
Gilbert Kerr, Gilberto González-Parra, Michele Sherman, “A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations”, Applied Mathematics and Computation, 420 (2022), 126914
Gilbert Kerr, Gilberto González-Parra, “Accuracy of the Laplace transform method for linear neutral delay differential equations”, Mathematics and Computers in Simulation, 197 (2022), 308
A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. II”, Journal of Mathematical Sciences, 130:6 (2005), 5083–5255
A. M. Sedletskii, “Bases of Exponentials in the Spaces $L^p(-\pi,\pi)$”, Math. Notes, 72:3 (2002), 383–397
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