Strong Approximation Of Fourier Series Research Articles

Strong approximation of Fourier series on generalized periodic Morrey spaces

Strong approximation of Fourier series on generalized periodic Morrey spaces

Groups of Deviations of the Fourier Series in Generalized Hölder Spaces

We study the rate of convergence of the values of analogs of the functionals of strong approximation of Fourier series in generalized L-Holder spaces.

Applications of general monotone sequences to strong approximation by Fourier series

We consider the strong means of Fourier series generated by infinite nonnegative triangular matrices and prove some estimates of such means in the case of a matrix with rows stating the sequences from the class GM(5β). Our theorems correspond to the results of L. Leindler [L. Leindler, A note on strong approximation of Fourier series, Anal. Math. 29 (2003) 195–199] and essentially extend the result of S.M. Mazhar and V. Totik [S.M. Mazhar, V. Totik, Approximation of continuous functions by T -means of Fourier series, J. Approx. Theory, 60 (1990) 174–182].

Embedding relations connected with strong approximation of Fourier series

We consider the embedding relation between the class WqHβω, including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl.11(4) (2008) 749–756] which is a generalization of Tikhonov’s results [Anal. Math.31 (2005) 183–194]. We also extend the Leindler theorem [Anal. Math.31 (2005) 175–182] concerning sequences of Fourier coefficients.

Embedding theorems in strong approximation of Fourier series

In this paper, we introduce some new classes of functions and investigate the embedding relations among these classes. Our results generalize the related results of Leindler [3] and Yu-Zhou [9].

Addendum to “Trigonometric series of Nikol’skii classes”

We describe the functions from Nikol’skii class in terms of behavior of their Fourier coefficients. Results for series with general monotone coefficients are presented. The problem of strong approximation of Fourier series is also studied.

Embedding results pertaining to strong approximation of Fourier series. VI

We verify a newer version of a certain embedding theorem pertaining to the relation being between strong approximation and a certain wide class of continuous functions. We also show that a new class of numerical sequences defined in this paper is not comparable to the class defined by Lee and Zhou, which is one of the largest among the classes being extensions of the class of monotone sequences.

A note on strong approximation of Fourier series and embedding theorems

A note on strong approximation of Fourier series and embedding theorems

Embedding results pertaining to strong approximation of Fourier series. V

Embedding results pertaining to strong approximation of Fourier series. V

Strong approximation of Fourier series and embedding theorems

In this paper, embedding results are considered which arise in the strong approximation by Fourier series. We prove several theorems on the interrelation between the classes Wr Hβω and H (λ,p,r,ω), the latter being defined by L. Leindler. Previous related results in Leindler’s book [2] and paper [5] are particular cases of our results.

Embedding results pertaining to strong approximation of Fourier series. IV

Embedding results pertaining to strong approximation of Fourier series. IV

A note on strong approximation of Fourier series

We generalize a theorem of Mazhar and Totik in two directions. We extend the set of their summability matrix and consider strong approximation instead of ordinary one.

Embedding results pertaining to strong approximation of fourier series. I

Embedding results pertaining to strong approximation of fourier series. I

Embedding results pertaining to strong approximation of fourier series. III

Embedding results pertaining to strong approximation of fourier series. III

Embedding results pertaining to strong approximation of fourier series. II

Embedding results pertaining to strong approximation of fourier series. II

Strong approximation by Fourier series

G. Freud had wide research interests which included Fourier series. In this survey paper we intend to show the great influence of his only paper [2] on strong approximation of Fourier series. This article has been the origin of a new subject called nowadays “converse-type results for strong approximation of Fourier series.” Before stating his initial result we outline briefly the background of the subject. After the classical result of Fejer in 1904 on the convergence of the arithmetical mean of the partial sums of a Fourier series of 2x-periodic functions, Hardy and Littlewood [3] began to investigate the problem of so-called strong summability. It turned out that under certain conditions not only the means

Notes on Fourier series: Strong approximation

Two results are proved about strong approximation of Fourier series. The first, which goes in the positive direction, is the best possible refinement of an inequality of L. Leindler. The second is related to the inverse problem and provides a unified treatment to many earlier results.

Additional results on the strong approximation of Fourier series

Первая цель работы — п олучить достаточное условие, выраженное в термина х некоторых свойств сильной аппр оксимации функций, пр и котором она принадлежит клас суWrHω без каких-либо ограни чений на модуль непре рывностиω.

Derivative functions and strong approximation of Fourier series. II

Derivative functions and strong approximation of Fourier series. II

On the strong approximation of Fourier series

On the strong approximation of Fourier series