共查询到20条相似文献,搜索用时 0 毫秒
1.
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
2.
利用函数的傅里叶展开式求级数的和 总被引:2,自引:0,他引:2
利用函数的傅里叶展开式可求得级数∞∑n=11/n2+λ2及∞∑n=1(-1)m/n2+λ2的和,而通过引入复数并利用欧拉公式可求得级数∞∑n=1 1/n2+λ2及∞∑n=1(-1)m/n2+λ2的和. 相似文献
3.
Avram Sidi 《Applied mathematics and computation》2010,216(11):3378-3385
In this work, we are concerned with the derivation of full asymptotic expansions for Fourier integrals as s → ∞, where s is real positive, [a, b] is a finite interval, and the functions f(x) may have different types of algebraic and logarithmic singularities at x = a and x = b. This problem has been treated in the literature by techniques involving neutralizers and Mellin transforms. Here, we derive the relevant asymptotic expansions by a method that employs simpler and less sophisticated tools. 相似文献
4.
对于周期函数f(x)按不同的周期展开对应不同的Fourier级数,这些表面上不同的式子是否一致引起了人们的注意[1],[2].本文应用Parseval等式给出一个关于这种唯一性的简单证明,并把这一种性质推广到高维情况的多重Fourier级数. 相似文献
5.
Hiro-O Kitax 《Mathematische Nachrichten》1998,193(1):57-74
Let S* (f be the majorant function of the partial sums of the trigonometric Fourier series of f. In this paper we consider the Orlicz space Lπ and give a generalization of Soria's result [S1]. Let π (t) be a concave function with some nice properties and . If there exists a positive constant a0 < 1 such that then we have . 相似文献
6.
Camil Muscalu 《Proceedings of the American Mathematical Society》1997,125(2):541-546
Let be a rearrangement invariant space, an arbitrary set and a von Neumann algebra with a semifinite normal faithful trace. It is proved that the associated symmetric space of measurable operators has -RNP if and only if has -RNP extending in this way some previous results by Q. Xu.
7.
S. E. Kholodovskii 《Computational Mathematics and Mathematical Physics》2008,48(7):1140-1144
In the framework of the theory of harmonic functions, potentials of steady state processes (heat conduction, filtration, or electrostatics) in the piecewise inhomogeneous plane separated by a rectilinear strongly permeable crack or by a weakly permeable screen into two half-planes with quadratic permeability functions are constructed. The motion is induced by given singular points of the potential (sources, sinks, etc.). Compact formulas that directly express potentials in these domains in terms of harmonic functions are obtained; the resulting functions map the set of harmonic functions to the set of potentials conserving the type of singularities. 相似文献
8.
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
9.
E. D. Nursultanov 《Mathematical Notes》1998,63(2):205-214
In this paper we prove theorems on multiplicators of Fourier series inL
p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998. 相似文献
10.
V.S. Serov 《Journal of Mathematical Analysis and Applications》2007,329(1):132-144
We study the degenerate elliptic differential operator of the second order in the divergence form. The operator is assumed to be symmetric. The weight function which is describing the degeneration of the coefficients (or singularity) assumed to be in the Muckenhoupt class. We prove the uniform estimates for the fundamental solution of this operator and obtain the conditions which guarantee the absolute and uniform convergence of Fourier series in eigenfunctions. These results might be applied to the ground of Fourier method. 相似文献
11.
Dansheng Yu Ping Zhou Songping Zhou 《Journal of Mathematical Analysis and Applications》2008,341(1):12-23
In this paper, we generalize some well-known results (Theorems A, C, and D) by establishing two general results (Theorems 1 and 3). As special applications, we find that the (generalized) jumps of f can be determined by the higher order partial derivatives of its Abel-Poisson means. This is different from the determination of jumps by higher order derivatives of the partial sums. We also give some estimates of the higher order partial derivatives of the Abel-Poisson mean of an integrable function F at those points at which F is smooth. 相似文献
12.
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
13.
Evgeniy Pustylnik 《Czechoslovak Mathematical Journal》2001,51(3):561-572
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations. 相似文献
14.
A model for the formation of a “crust” during bread baking is presented. The crust is the outermost part of the loaf where the final bread density is significantly higher than in the “crumb”, the interior of the loaf. The model is based on a collapse mechanism, whereby raised pressures due to thermal expansion and water evaporation squash bubbles in the bread as the dough sets and fractures; the latter process allows vapour within bubbles to escape. 相似文献
15.
The problem originates from the necessity to predict luminosities of large-amplitude variable stars that are to be observed by the astronomical satellite HIPPARCOS. The data have a specific character: they are unequally time-spaced and can be missing during a long time in comparison to the pseudo-period. So the classical method of time-series analysis must be adapted and new methods are to be searched. In this paper we present a numerical solution derived from a Fourier analysis. 相似文献
16.
S. E. Kholodovskiĭ 《Computational Mathematics and Mathematical Physics》2007,47(9):1489-1495
An efficient method of construction of solutions to a set of boundary value problems with additional interface conditions, more complicated boundary conditions, and so on on the basis of known solutions to classical boundary value problems is proposed. The method is based on the representation of solutions to classical and more complicated problems in the form of expansions into Fourier series with subsequent reduction of one series to the other. As a result, formulas directly expressing solutions to more complicated problems in terms of solutions to classical problems are obtained. On the basis of the well-known solution to the Dirichlet problem on a half plane, solutions to boundary value problems with interface conditions (including generalized conditions of the type of a crack and a screen) on intersecting straight lines for boundary conditions of the first and the third kind are obtained. 相似文献
17.
Stephen P. Huestis 《Numerical Methods for Partial Differential Equations》2001,17(6):673-683
Introducing an electric conductor into a region pervaded by an initial electric potential perturbs that potential by inducing a charge distribution on the conductor's surface, necessary to guarantee that the surface is an equipotential of the total potential. Some numerical method is required to compute the perturbation potential, when the conductor's shape does not admit a standard analytic solution. For two‐dimensional situations, a method is proposed for solving for the perturbation potential that involves expansion of the boundary perturbation potential and its normal derivative as truncated Fourier series. This boundary potential is known to within an additive constant from the requirement that its sum with the initial potential must be a constant. The standard representation theorem for the Dirichlet problem gives a consistency relation between the boundary function and its normal derivative, which here becomes a set of linear algebraic relations between Fourier series coefficients, with matrix entries found by appropriate applications of the fast Fourier transform. These are solved for the boundary derivative coefficients; at any point exterior to the conductor, the perturbation potential can then be evaluated from the two sets of Fourier coefficients, using further application of the fast Fourier transform. Examples are shown for two conductor shapes, with several initial potentials. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 673–683, 2001 相似文献
18.
John P. Boyd 《高等学校计算数学学报(英文版)》2013,6(4):586-599
We show that the zeros of a trigonometric polynomial of degree $N$ with the usual $(2N +1)$ terms can be calculated by computing the eigenvalues of a matrix of dimension $2N$ with real-valued elements $M_{jk}$.
This matrix $\vec{\vec{M}}$ is a multiplication matrix in the sense that, after first defining a vector $\vec{\phi}$ whose elements are the first $2N$ basis functions, $\vec{\vec{M}}\vec{\phi}$ = 2cos($t$)$\vec{\phi}$.
This relationship is the eigenproblem; the zeros $t_{k}$ are the arccosine function of $\lambda_{k}/2$ where the $\lambda_{k}$ are the eigenvalues of $\vec{\vec {M}}$. We dub this the "Fourier Division Companion Matrix'', or FDCM for short, because it is derived using trigonometric polynomial division. We show through examples that the
algorithm computes both real and complex-valued roots, even double roots, to near machine precision accuracy. 相似文献
19.
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