共查询到20条相似文献,搜索用时 109 毫秒
1.
In this paper, we obtain five tests (three of which are symmetric) of pointwise convergence of Fourier series with respect to generalized Haar systems; the tests are similar to the Dini convergence tests. It is shown that the Dini convergence tests for Price systems are also valid for generalized Haar systems. It is also shown that the classicalDini convergence test does not apply, in general, even to generalized Haar systems, although the classical symmetric Dini test for generalized Haar systems is valid. Also upper bounds for the Dirichlet kernels for generalized Haar systems are obtained. 相似文献
2.
We consider Fourier coefficients for functions of bounded variation with respect to general orthonormal systems (GONS). We show that in general case the sequence of coefficients may have an arbitrarily prescribed order of vanishing. In this connection we seek for a class of GONS such that Fourier coefficients of a function from V(0, 1) satisfy the same inequality as in the case of classical systems (trigonometric, Walsh, and Haar ones). In the present paper we study this problem and related issues. 相似文献
3.
Peter Hellekalek 《Monatshefte für Mathematik》1995,120(1):25-45
The classical Erdös-Turán-Koksma inequality gives us an upper bound for the discrepancy of a sequence in thes-dimensional unit cube in terms of exponential sums, more precisely, in terms of the trigonometric function system.In this paper, we shall prove the inequality of Erdös-Turán-Koksma for the extreme and the star discrepancy, for generalized Haar function systems. Further, we shall show the existence of the inequality of Erdös-Turán-Koksma for the isotropic discrepancy, for generalized Haar and Walsh function systems.Research supported by the Austrian Science Foundation, project no. P9285/TEC. 相似文献
4.
We consider a series with respect to a multiplicative Price system or a generalized Haar system and assume that the martingale subsequence of its partial sums converges almost everywhere. In this paper we prove that, under certain conditions imposed on the majorant of this sequence, the series is a Fourier series in the sense of the A-integral (or its generalizations) of the limit function if the series is considered as a series with respect to a system with supp
n < . In similar terms, we also present sufficient conditions for a series to be a Fourier series in the sense of the usual Lebesgue integral. We give an example showing that the corresponding assertions do not hold if supp
n = . 相似文献
5.
In this paper we establish the Haar and Walsh systems on a triangle. These systems are complete in $L_2(\Delta)$. The uniform convergence of the Haar-Fourier series and the uniform convergence by group of the Walsh-Fourier series for any continuous function are proved. 相似文献
6.
It is well known that the Fourier coefficients of continuous functions with respect to classical orthogonal systems (trigonometric, Haar, and Walsh) can be estimated via the moduli of continuity of the functions. However, not all orthonormal systems possess this property. We obtain necessary and sufficient conditions on orthonormal systems such that the Fourier coefficients of continuous functions with respect to these orthonormal systems can be estimated via the moduli of continuity in a certain sense. 相似文献
7.
G. A. Akishev 《Russian Mathematics (Iz VUZ)》2009,53(11):1-8
In this paper we establish conditions for the absolute convergence of series of Fourier coefficients with respect to a generalized
Haar system of a superposition of two functions. 相似文献
8.
Gottlieb Pirsic 《Monatshefte für Mathematik》2001,12(1):153-168
For an orthonormal basis (ONB) of we define classes of functions according to the order of decay of the Fourier coefficients with respect to the considered ONB . The rate is expressed in the real parameter α. We investigate the following problem: What is the order of decay, if any, when we consider with respect to another ONB ? If the function is expressable as an absolutely convergent Fourier series with respect to , we give bounds for the new order of decay, which we call . Special attention is given to digital orthonormal bases (dONBs) of which the Walsh and Haar systems are examples treated in the present paper. Bounding intervals and in several cases explicit values for are given for the case of dONBs. An application to quasi-Monte Carlo numerical integration is mentioned. 相似文献
9.
Gottlieb Pirsic 《Monatshefte für Mathematik》2001,132(2):153-168
For an orthonormal basis (ONB) of we define classes of functions according to the order of decay of the Fourier coefficients with respect to the considered ONB . The rate is expressed in the real parameter α. We investigate the following problem: What is the order of decay, if any,
when we consider with respect to another ONB ? If the function is expressable as an absolutely convergent Fourier series with respect to , we give bounds for the new order of decay, which we call . Special attention is given to digital orthonormal bases (dONBs) of which the Walsh and Haar systems are examples treated
in the present paper. Bounding intervals and in several cases explicit values for are given for the case of dONBs. An application to quasi-Monte Carlo numerical integration is mentioned.
(Received 21 February 2000; in revised form 19 October 2000) 相似文献
10.
V. A. Rodin 《Mathematical Notes》1998,63(4):533-541
In this paper we establish a general assertion relating the oscillation of the sequence of rectangular partial sums of a multiple Fourier series in a multiplicative system to the strong summability of this series. The systems of group generators are assumed to be uniformly bounded. Earlier these assertions were obtained by the author for the Walsh and Chrestenson series.Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 607–616, April, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00135. 相似文献
11.
12.
Pedro J. Catuogno Sebastian E. Ferrando Alfredo L. Gonzalez 《Journal of Fourier Analysis and Applications》2008,14(5-6):712-743
H-systems are those orthonormal systems which allow computation of conditional expectations via a Fourier expansion. These systems provide natural approximations to continuous stochastic processes and we indicate how they could be used to perform lossy compression on a set of given signals. More specifically, we show how to construct, for a given random variable, an adaptive martingale approximation by means of generalized Haar functions. We also indicate how the construction can be extended to a given random vector. A generalized multiresolution analysis algorithm is also described and numerical examples are provided. 相似文献
13.
V. A. Skvortsov 《Moscow University Mathematics Bulletin》2017,72(1):24-30
It is proved that for any Banach space each everywhere convergent Haar series with coefficients from this space is the Fourier–Haar series in the sense of Henstock type integral with respect to a dyadic differential basis. At the same time, the almost everywhere convergence of a Fourier–Henstock–Haar series of a Banach-space-valued function essentially depends on properties of the space. 相似文献
14.
Generalized Fourier transform on an arbitrary triangular domain 总被引:4,自引:0,他引:4
In this paper, we construct generalized Fourier transform on an arbitrary triangular domain via barycentric coordinates and PDE approach. We start with a second-order elliptic differential operator for an arbitrary triangle which has the so-called generalized sine (TSin) and generalized cosine (TCos) systems as eigenfunctions. The orthogonality and completeness of the systems are then proved. Some essential convergence properties of the generalized Fourier series are discussed. Error estimates are obtained in Sobolev norms. Especially, the generalized Fourier transforms for some elementary polynomials and their convergence are investigated.
This work was supported by the Major Basic Project of China (No. G19990328) and National Natural Science Foundation of China (No. 60173021). 相似文献
15.
The second author recently introduced modified Walsh–Dirichlet kernels which generated filtered Walsh–Fourier series. The purpose of this article is to show that those filtered Walsh series can be generated by a partial ordering on the natural numbers which may be of interest in its own right. 相似文献
16.
P.A. Morettin 《Stochastic Processes and their Applications》1974,2(2):183-193
This paper is concerned with investigating the use of the orthonormal system of Walsh functions in the analysis of a dyadic-stationary series. The main emphasis is on the finite Walsh transform of a sequence of values coming from such a series. Under a certain mixing condition, given in terms of the dyadic auto-covariance function of the series, we derive a central limit theorem for the finite Walsh transform. This, in turn, allows us to consider estimates of the Walsh spectrum, and we discuss briefly the Walsh periodogram. 相似文献
17.
A uniqueness theorem and a recovery theorem for the coefficients of series in generalized Haar systems are proved under the assumption that the series converge in measure and satisfy a certain necessary condition on the distribution function of the majorant of partial sums. 相似文献
18.
In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible. 相似文献
19.
V. A. Skvortsov 《Mathematical Notes》1968,4(1):509-513
We set out the connection between convergence of the Haar series and differentiation with respect to nets of a function. This connection allows us to give a new proof of certain earlier theorems on Haar series, and also to prove a number of new generalizations.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 33–40, July, 1968.In conclusion we remark that the results we have proved here for the Haar series can be extended to the series in Haar-type systems considered at the end of [4]. 相似文献
20.
Analysis Mathematica - In this article we discuss the behaviour of Θ-means of Walsh—Fourier series of a function in dyadic Hardy spaces Hp and dyadic homogeneous Banach spaces X. Namely,... 相似文献