Some Approximation Properties of Series with Nonlinear Fourier Basis

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

The order of approximation of generalized de la Vallée Poussin means of series with nonlinear Fourierbasis was investigated in uniform and Hölder norms.

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[1] DeVore, R. A. and Lorentz, G., Constructive Approximation, Springer-Verlag. New York, 1993.
[2] Holland, A. S. B., A survey of degree of approximation of continuous functions. SIAM Rev. 23 (1981), 344-379.
[3] Huang, C. and Yang L., Approximation by the nonlinear Fourier basis. Sci. China Math. 54 (2011), 1207-1214.
[4] Leindler, L., On summability of Fourier series. Acta Sci. Math. Szeged 29 (1968), 147-162.
[5] Leindler, L., Meir, A. and Totik, V., On approximation of continuous functions in Lipschitz norms. Acta Math. Hung 45 (1985), 441-443.
[6] Prössdorf, S., Zur konvergenz der Fourierreihen hölderstetiger funktionen. Math. Nachr. 69 (1975), 7-14.
[7] Qian, T., Analytic signals and harmonic measures. J. Math. Anal. Appl. 314 (2006), 526-536.
[8] Qian, T. and Chen, Q., Characterization of analytic phase signals. Comput. Math. Appl. 51 (2006), 1471-1482.
[9] Stypinski, Z., On a generalization of the theorem of Prössdorf. Funct. Approx. Comment. Math. 7 (1979), 101-104.
[10] Timan, A. F., Theory of approximation of functions of a real variable, Pergamon Press, 1963.
[11] Zygmund, A., Trigonometric series, Vols. I-II, 2nd edition, Cambridge Univ. Press, London, 1959.