Strong uniform approximation by double Fourier series
نویسندگان
چکیده
منابع مشابه
On the uniform approximation of discrete-time systems by generalized Fourier series
In this paper, model sets for linear time-invariant discrete-time systems spanned by fixed orthonormal bases are studied. It is shown that the Fourier series of the system transfer function with respect to these bases converges uniformly on the unit circle if the frequency response of the system is Dini-Lipschitz continuous.
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 کاملApproximation by Nörlund Means of Double Walsh–fourier Series for Lipschitz Functions
For double trigonometric Fourier series, Móricz and Rhoades studied the rate of uniform approximation by Nörlund means of the rectangular partial sums of double Fourier series of a function belonging to the class Lipα (0 < α 1) [12] and the class of continuous functions [13], on the two-dimensional torus. As a special case, they obtained the rate of uniform approximation by double Cesàro means....
متن کاملOn 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 کاملThe Approximation by Partial Sums of Fourier Series
uniformly in x as h—»0, we shall say briefly that/ belongs to Lip a. Following 4](1)) we shall say that/ belongs to a) uniformly as *—>0. a notation already used (see Zygmund lipa, 0<a<l, if \f(x+h)-f(x)\=o(\h It is a classical result of Lebesgue (see Zygmund [5, p. 61 ] ; hereafter this book will be denoted by T.S.) that if / belongs to Lip a and if sn denotes the nth partial sum of the Fourie...
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: 1990
ISSN: 0021-9045
DOI: 10.1016/0021-9045(90)90021-h