Convergence of Fourier series on the systems of rational functions on the real axis
- Authors: Chaichenko S.O.1
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Affiliations:
- Donbas State Pedagogical University
- Issue: Vol 214, No 2 (2016)
- Pages: 229-246
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237364
- DOI: https://doi.org/10.1007/s10958-016-2771-8
- ID: 237364
Cite item
Abstract
The systems of rational functions {Φn(z)}, n ∈ ℤ; that are orthonormalized on the real axis ℝ and are defined by the fixed set of points a := {ak}k = 0∞, (Im ak > 0) and b := {bk}k = 1∞, (Im bk < 0); are considered. Some analogs of the Dirichlet kernels of the systems {Φn(t)}, n ∈ ℤ; on the real axis ℝ are given in a compact form, and the convergence in the spaces Lp(ℝ); p > 1; and the pointwise convergence of Fourier series on the systems {Φn(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.
About the authors
Stanislav O. Chaichenko
Donbas State Pedagogical University
Author for correspondence.
Email: s.chaichenko@gmail.com
Ukraine, Slavyansk