On the approximation of Fourier series by Abel means
نویسندگان
چکیده
منابع مشابه
On Measure of Approximation by Means of Fourier Series
A many of approximation methods in C2 (Fej er, de la Vall ee Poussin etc.) may be generated via a certain function ' 2 C[0;1] with '(0) = 1, '(1) = 0. The function 'j(t) = cos(j 1=2) t (j 2 N) generates the Rogosinski approximation method [N. K. Bari, "A Treatise on Trigonometric Series," I, II, Pergamon Press, 1964]. Our idea consists in representing ' by the orthogonal system 'j to extend res...
متن کاملOn the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series
Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has ...
متن کاملOn the degree of approximation of continuous functions by means of Fourier series ∗
We generalize some results on the degree of approximation of continuous functions by means of Fourier series, which were obtained by Chandra ([1, 2]) and Leindler ([4]). Some applications of the main results are given. AMS subject classifications: 42A24, 41A25
متن کاملOn the Approximation Properties of Cesàro Means of Negative Order of Walsh-Fourier Series
In this paper we establish approximate properties of Cesàro (C,−α)-means with α ∈ (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ−α n (f, x) to f (x) in the L p-metric. We also show that this condition cannot be improved in the case p = 1.
متن کاملDetermination of a jump by Fourier and Fourier-Chebyshev series
By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounded variation. This is achieved without the finiteness assumption on the number of discontinuities. Two results on determination of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1972
ISSN: 0021-9045
DOI: 10.1016/0021-9045(72)90040-8