共查询到20条相似文献,搜索用时 46 毫秒
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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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Fourier级数部分和对ω-型单调函数的逼近 总被引:7,自引:0,他引:7
俞国华 《高校应用数学学报(A辑)》2002,17(1):51-55
引入ω-型单调函数的概念,研究了Fourier级数部分和对其的逼近问题,推广了Mazhar(1991)的结果,减弱了Salem和Zygmund(1946)的结果的条件,使Salem和Zygmund的结论适用于更大的函数类。 相似文献
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我们定义了(H,λ)求和法,它含有(N,pn),(R^rn)和(Vmn)求和法。讨论了函数f(x)∈C^r[-1,1](r∈N0)以及f(x)∈W^rH^a(r∈N0,0<a<1)的切比晓夫-富里埃级数的逼近阶。 相似文献
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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
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Fourier级数的求和理论与方法—求和因子法求和 总被引:5,自引:0,他引:5
在 Fourier级数的线性求和中 ,通过构造求和因子 ,使得带有该求和因子的积分算子在全轴上一致地收敛到每个以 2 π为周期的连续函数 ,并对 Cj2π(0 j r)函数类的逼近均达到最佳收敛阶 ,参数 r为任意给定的奇自然数 . 相似文献
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研究了拟Fourier-Jacobi级数逐项求导后所得的导级教,给出了一个等价收敛定理. 相似文献
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设un为n阶酉群。u∈L1(Un)的Fourier级数的第二型Cesáro平均为σNα(u,U)=KN*αu(U),其中 KNα(U)=sum from (N≥li>…>ln≥-N)(Al1α…A1uN(f)Xf(U)),U∈Un为相应的核函数。本文给出“Lebesgue常数”‖KNα‖(L1(Un))的精确估计,并由此建立了酉群上函数的Fourier级数按第二型Cesáro求和收敛于自身的条件。 相似文献
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In this article we prove that if the coefficients of a Fourier-Legendre expansion satisfy a suitable Hausdorff-type condition,
then the series converges to a function which admits a holomorphic extension to a cut-plane. Furthermore, we prove that a
Laplace-type (Laplace composed with Radon) transform of the function describing the jump across the cut is the unique Carlsonian
interpolation of the Fourier coefficients of the expansion. We can thus reconstruct the discontinuity function from the coefficients
of the Fourier-Legendre series by the use of the Pollaczek polynomials. 相似文献
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Jian Li & Ben-Yu Guo 《计算数学(英文版)》1995,13(2):144-155
1.IntroductionThenumericalmethodsoftheNavier-Stokesequationscanbefoundin[1-4].Spe-cificalgorithmsin[5-8]havebeendevotedtothesemi-periodiccaseswhichdescribechannelflow,parallelboundarylayers,curvedchannelflowandcylindricalCouettenow.Inthispaper5weconsiderthemiredFourier-LegendrespectralaPproximationfortheunsteadyNavier-Stokesequations-WeuseFourierspectralapprokimationintheperiodicdirectionsandLegendrespectralapproximationinthenon-periodicone.Forapproximatingcontinuityequation,weadoptsmanPa… 相似文献
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Let f(x) be a periodic function of period 2π,|f(x)|and |f(x)|p integrable on [0,2π].It is said to be f∈HX1,if (∫02π|f(x+h)-f(x)|pdx)1/p≤|h|.It is said to be f∈HX2,if (∫02π|f(x+h)+f(x-h)-2f(x)|pdx)1/p≤2|h|. 相似文献
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For the convergence of double series and iterated series, a sufficient condition is obtained. This result provides a test for the convergence of double series and iterated series. 相似文献
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D. S. Kataev 《Journal of Mathematical Sciences》2002,110(6):3091-3110
We study cubic metaplectic Eisenstein series connected with the Jacobi maximal parabolic subgroup of a symplectic group. We use the so-called ``sl(2)-triples' technique in order to evaluate the Fourier coefficients of these series. In Secs. 1 and 2, we introduce the necessary notation and study the group
and its subgroups in detail. In Sec. 3, we prove the main result of the present paper (Theorem 1). Section 4 is devoted to the study of the Dirichlet series appearing in Theorem 1. Bibliography: 5 titles. 相似文献
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This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic. 相似文献