On the Absolute Convergence of Lacunary Fourier Series
Copyright policy )On the Absolute Convergence of Lacunary Fourier Series
In 1958, P. B. Kennedy [2] proved a two-part theorem on the order of magnitude of the coefficients and the absolute convergence of lacunary Fourier series, and he conjectured that his conclusions remained valid under weaker conditions. The conjecture on the order of magnitude of the coefficients was established by M. and S. I. Izumi [1]. In this note the second half of the conjecture, concerning absolute convergence, is deduced from a recent result of Patadia [3].
Best approximation, Chebyshev systems, absolute convergence, Trigonometric approximation, Convergence and absolute convergence of Fourier and trigonometric series, trigonometric polynomials, Summability and absolute summability of Fourier and trigonometric series, lacunary Fourier series, Lacunary series of trigonometric and other functions; Riesz products, Fourier series, best approximation
Best approximation, Chebyshev systems, absolute convergence, Trigonometric approximation, Convergence and absolute convergence of Fourier and trigonometric series, trigonometric polynomials, Summability and absolute summability of Fourier and trigonometric series, lacunary Fourier series, Lacunary series of trigonometric and other functions; Riesz products, Fourier series, best approximation
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