共查询到20条相似文献，搜索用时 0 毫秒
1.
Pamela B. Pierce Daniel Waterman 《Proceedings of the American Mathematical Society》2000,128(9):2593-2596
It is shown that the concept of bounded variation in the mean is not a meaningful generalization of ordinary bounded variation. In fact, it is a characterization of functions which differ from functions of bounded variation on a zero set.
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给出共轭Neumann-Bessel级数的核函数的渐近表达式，它的精度达到O（），然后利用这个表达式，讨论了该级数的收敛速度． 相似文献
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本文把Fourier级数的一些经典结论推广到有理Fourier级数的情况下. 首先给出了有理Fourier级数和共轭有理Fourier级数在有界变差条件下的收敛速度估计. 利用此结论, 得到了类似于Fourier级数的Dirichlet-Jordan定理和W. H. Young定理. 最后, 证明了这两个定理在调和有界变差条件下也成立. 相似文献
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The double Fourier series of functions of the generalized bounded variation class are shown to be Pringsheim convergent everywhere. In a certain sense, this result cannot be improved. In general, functions of class defined here, have quadrant limits at every point and, for there exist at most countable sets and such that, for and is continuous at . It is shown that the previously studied class contains essentially discontinuous functions unless the sequence satisfies a strong condition.
5.
本注记给出了关于在Fourier级数L~1收敛中MVBV条件不可减弱的一个猜想的肯定回答。 相似文献
6.
Jeffery D. McNeal Yunus E. Zeytuncu 《Journal of Mathematical Analysis and Applications》2006,323(2):1348-1353
We give an example of a permutation of integers which preserves all convergent Fourier series and makes some divergent Fourier series converge. 相似文献
7.
Michael E. Taylor 《Proceedings of the American Mathematical Society》2001,129(7):2001-2003
In this note we complete a circle of results presented in §5 of an earlier work of the author (J. Fourier Anal. 5 (1999), 449-463), establishing the endpoint case of Proposition 10 of that paper. As a consequence, we have results on pointwise convergence of the Fourier series (summed by spheres) of a function on the 3-dimensional torus with a simple jump across a smooth surface , with no curvature hypotheses on , extending Proposition 7 of that paper.
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Katusi Fukuyama Shigeru Takahashi 《Proceedings of the American Mathematical Society》1999,127(2):599-608
In this paper, the central limit theorem for lacunary trigonometric series is proved. Two gap conditions by Erdos and Takahashi are extended and unified. The criterion for the Fourier character of lacunary series is also given.
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单调性条件在Fourier级数收敛性中的最终推广:历史、发展、应用和猜想 总被引：1，自引：0，他引：1
为了对Fourier级数进行近似计算和有效应用,必须研究其收敛性,这个课题有长久的历史,形成了数学分析中吸引包括许多著名数学家在内的学者研究的一条热烈但困难的主流.其中,在三角级数(Fourier级数)一致收敛性和平均收敛性问题中人们一直关心Fourier系数的单调递减条件最终的推广.这个开始于英国Chaundy-Jollife(1916年)和Young(1913年)的工作最近出现了突破性的进展,产生了许多完善的结果.本文将对这方面的历史、发展给出综述,并重点介绍最近的应用成果,并对以后的工作给出研究思路和线索. 相似文献
10.
S. Baron E. Liflyand U. Stadtmüller 《Journal of Mathematical Analysis and Applications》2000,250(2):226
Complementary spaces for Fourier series were introduced by G. Goes and generalized by M. Tynnov. In this paper we investigate a notion of complementary space for double Fourier series of functions of bounded variation. Various applications are given. 相似文献
11.
Taylor级数与Fourier级数是两类非常重要的函数项级数,二者在发展与应用背景、展开条件、收敛性和展开的唯一性等方面不尽相同,本文对此作了一些总结与探讨。 相似文献
12.
Eugene Shargorodsky 《Mathematische Nachrichten》1997,183(1):229-273
Some methods are described for reducing the problem of the boundedness of pseudodifferential operators (ΨDOs) to the theory of Fourier multipliers. Special attention is given to the boundedness of ΨDOs in Besov - Triebel - Lizorkin spaces. 相似文献
13.
本文给出加权 Ｐｌａｎｃｈｅｒｅｌ公式与Ｈｅｒｍｉｔｅ对称空间上的齐性线从上Ｐｌａｎｃｈｅｒｅｌ公式的关系,由此导出一般有界对称域上的加权Ｐｌａｎｃｈｅｒｅｌ公式． 相似文献
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Mathematical Notes - 相似文献
15.
H. Germano Pavão 《International Journal of Mathematical Education in Science & Technology》2013,44(7):961-967
We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. 相似文献
16.
Nicola Fusco Daniel Spector 《Journal of Mathematical Analysis and Applications》2018,457(2):1370-1375
In this paper, we show how under the continuum hypothesis one can obtain an integral representation for elements of the topological dual of the space of functions of bounded variation in terms of Lebesgue and Kolmogorov–Burkill integrals. 相似文献
17.
Don Galagedera George Woodward Sunanda Degamboda 《International Journal of Mathematical Education in Science & Technology》2013,44(5):679-689
This study investigates the effects of perceived mathematics ability (PMA) on the learning process with special reference to 147 undergraduates following an elementary statistics (ES) course. A model incorporating PMA together with aptitude, effort put in, expected grade, motivation to do well and interest in the subject, which are deemed to be either directly or indirectly associated with performance, is developed. PMA itself is not a good predictor of ES performance, rather its effect may be channelled through interest, expected grade and motivation to do well in ES. Low perception in mathematics ability impedes effort put forth when learning ES. The influence of PMA on ES performance is likely to be the consequence of the belief that mathematics is essential to learn ES. 相似文献
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《Integral Transforms and Special Functions》2012,23(1):33-40
It's an old idea which goes back essentially to Fourier's pioneering works on the suject, to establish a direct connection between Fourier's double integral and the ordinary fourier series of the pertinent function. But this point of view remained a heuristic expedient up to now, and the rigorous foundation of Fourier transforms was built on the whole independently of the convergence theory of Fourier series-though naturally on the analogy of this field. The situation is somewhat similar also about the elegant results of Plancherel concerning square integrable functions and convergence in mean. In th paper [4] written in German, the author has dealed with some exact results of this kind, which will appear in more detailed form in the chapter on Fourier integrals of the monograph [5]. The present paper aims to summing up the most general devlopments found recently about the problem, together with certain applications. (See Theorems 1.-3). 相似文献