Abstract
The systems of rational functions {Φ n (z)}, n ∈ ℤ; that are orthonormalized on the real axis ℝ and are defined by the fixed set of points a := {a k } ∞ k = 0 , (Im a k > 0) and b := {b k } ∞ k = 1 , (Im b k < 0); are considered. Some analogs of the Dirichlet kernels of the systems {Φ n (t)}, n ∈ ℤ; on the real axis ℝ are given in a compact form, and the convergence in the spaces L p (ℝ); p > 1; and the pointwise convergence of Fourier series on the systems {Φ n (t)}, n ∈ ℤ; are studied under the certain restrictons on the sequences of poles of these systems. Some analogs of the classical Jordan–Dirichlet and Dini–Lipschitz criteria of convergence of Fourier series in a trigonometric system are constructed.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 3, pp. 403–426, July–August, 2015.
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Chaichenko, S.O. Convergence of Fourier series on the systems of rational functions on the real axis. J Math Sci 214, 229–246 (2016). https://doi.org/10.1007/s10958-016-2771-8
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DOI: https://doi.org/10.1007/s10958-016-2771-8