共查询到20条相似文献,搜索用时 31 毫秒
1.
本文研究连续窗口Fourier变换的反演公式.与经典的积分重构公式不同,本文证明当窗函数满足合适的条件时,窗口Fourier变换的反演公式可以表示为一个离散级数.此外,本文还研究这一重构级数的逐点收敛及其在Lebesgue空间的收敛性.对于L^2空间,本文给出重构级数收敛的充分必要条件. 相似文献
2.
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
3.
E. S. Belinsky 《Journal of Approximation Theory》2001,110(2):229
We estimate the metric entropy of compact subsets of the algebra A of absolutely convergent Fourier series 相似文献
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Letf be a continuous function on the unit circle Γ, whose Fourier series is ω-absolutely convergent for some weight ω on the set
of integersZ. If f is nowhere vanishing on Γ, then there exists a weightv onZ such that 1/f hadv-absolutely convergent Fourier series. This includes Wiener’s classical theorem. As a corollary, it follows that if φ is holomorphic
on a neighbourhood of the range off, then there exists a weight Χ on Z such that φ ◯f has Χ-absolutely convergent Fourier series. This is a weighted analogue of Lévy’s generalization of Wiener’s theorem. In
the theorems,v and Χ are non-constant if and only if ω is non-constant. In general, the results fail ifv or Χ is required to be the same weight ω. 相似文献
6.
Peter Schiavone 《Applicable analysis》2013,92(1-4):263-274
In this paper we show how to construct fundamental sequences for approximate solutions to exterior Dirichlet and Neumann-type problems in the bending of micropolar plates. The sequences are based on singular solutions of the governing equilibrium equations. These singular solutions are, however, unbounded at infinity. This leads to difficulties when applying the usual methods for proving linear independence and completeness. By decomposing the sequences into divergent and convergent parts we show that they can be accommodated in a more general framework developed in previous work. This allows us to overcome the difficulties mentioned above. Kupradze's method of generalised Fourier series is then modified and used to construct approximations which converge uniformly to the corresponding exact solutions 相似文献
7.
Abdellah El Kinani 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):343-352
We obtain weighted algebra analogues of the classical theorems of N. Weiner and P. Lévy on absolutely convergent Fourier series
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8.
Haseo Ki 《Proceedings of the American Mathematical Society》1996,124(11):3507-3514
In this article we calculate the exact location in the Borel hierarchy of the set of all continuous functions on the unit circle with uniformly convergent Fourier series. It turns out to be complete Also we prove that any set that includes must contain a continuous function with divergent Fourier series.
9.
P. LefèvreD. Li H. QueffélecL. Rodr?&#x;guez-Piazza 《Journal of Functional Analysis》2002,188(1):272-291
We investigate translation invariant subspaces of the space of uniformly convergent Fourier series and Orlicz spaces, with finite cotype. In the case of Orlicz spaces, this leads to some new characterizations of p-Rider sets. 相似文献
10.
A result of B.B. Wells Jr. claims that every complex valued continuous function on the compact ring of p-adic integers has a rearrangement which belongs to a certain class (W) of functions having absolutely convergent Fourier series. We point out that this is not the case since every real valued function from (W) has Lebesgue null range. On the other hand we prove the existence of a rearrangement with absolutely convergent Fourier series for every continuous real valued function on and on some other compact metric totally disconnected Abelian groups. We leave open if the same holds for all continuous complex valued functions on . 相似文献
11.
Jean M.‐S. Lubuma 《Numerical Methods for Partial Differential Equations》2008,24(3):699-727
The exterior Stokes problem between two parallel planes that are separated by a prismatic cylinder is extended to the interior of the prism by requiring the continuity of the velocity across the lateral faces. The well‐posedness of the exterior–interior problem is proved in suitable weighted Sobolev spaces. The solution is represented by Fourier series in the z‐variable. The Fourier coefficients, solutions of auxiliary two‐dimensional exterior–interior problems, are analyzed by viewing them as boundary integral equations of potential theory and global regularity of the densities, is established in weighted Sobolev spaces of traces. A boundary element method, with suitably refined mesh size, is implemented for the numerical treatment of the Fourier coefficients. This provides optimal convergent semi‐ and fully‐discrete spectral methods of Fourier–Galerkin type. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
12.
W. Sun 《Mathematische Nachrichten》2012,285(7):914-921
In this paper, we study the inversion formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an inversion formula which is known in engineering. We show that the integral involved in the formula is convergent almost everywhere on $\mathbb {R}$ as well as in Lp for all 1 < p < ∞ if the function to be reconstructed is. 相似文献
13.
Z. Ditzian 《Rendiconti del Circolo Matematico di Palermo》1936,60(1-2):99-106
The classical Bernstein estimate for absolutely convergent Fourier series and its multivariate extension are improved. Analogous results for absolutely convergent expansion by Legendre polynomials and by spherical harmonic polynomials are given. For expansion by a Fourier series it follows that the present result implies the classical result. Moreover, there are many functions that are shown to have an absolutely convergent Fourier series using the present estimate while not satisfying the conditions of the previous one. 相似文献
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Ferenc Móricz 《Journal of Mathematical Analysis and Applications》2008,342(2):1246-1249
We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs to one of the Zygmund classes Λ∗(α) and λ∗(α) for some 0<α?2. This paper is a natural supplement to our earlier one [F. Móricz, Absolutely convergent Fourier series and function classes, J. Math. Anal. Appl. 324 (2) (2006) 1168-1177] under the same title, and we keep its notations. 相似文献
16.
以 2 l为周期的函数 f(x)也可看作周期为 2 kl(k=1 ,2 ,3 ,… ) .设 f(x)满足 Dirichlet充分条件 ,[2 ]证明了按 [1 ]方法展开的以 2 l为周期的 Fourier级数和以 4l为周期的 Fourier级数对应的不同表达形式是一致的 .本文则在 [2 ]的基础上 ,进一步证明了按 [1 ]方法展开的以 2 l为周期的 Fourier级数和以 2 kl(k=1 ,2 ,3 ,… )为周期的 Fourier级数对应的表达式的一致性 ,从而得出结论 :任一周期函数 f(x)按 [1 ]方法展开的Fourier级数是唯一的 . 相似文献
17.
本文研究了复平面单位圆上的广义Fourier积分.利用经典的Fourier分析的结果和Carleson定理,以及复平面上解析函数在高阶导数下直角坐标和极坐标之间的关系,我们得到了前面定义的广义Fourier积分的一个收敛定理,从而推广了直线上经典Fourier积分的收敛结果. 相似文献
18.
Ravshan R. Ashurov 《Applicable analysis》2013,92(1):29-44
We consider two forms of eigenfunction expansions associated with an arbitrary elliptic differential operator with constant coefficients and order m, that is the multiple Fourier series and integrals. For the multiple Fourier integrals, we prove the convergence of the Riesz means of order s?>?(N???3)/2 of piecewise smooth functions of N?≥?2 variables. The same result is proved in the case of the N?≥?3 dimensional multiple Fourier series. 相似文献
19.
Hans Munthe-Kaas Tor Sørevik 《Applied Numerical Mathematics》2012,62(3):155-165
When multidimensional functions are approximated by a truncated Fourier series, the number of terms typically increases exponentially with the dimension s. However, for functions with more structure than just being L2-integrable, the contributions from many of the Ns terms in the truncated Fourier series may be insignificant. In this paper we suggest a way to reduce the number of terms by omitting the insignificant ones. We then show how lattice rules can be used for approximating the associated Fourier coefficients, allowing a similar reduction in grid points as in expansion terms. We also show that using a lattice grid permits the efficient computation of the Fourier coefficients by the FFT algorithm. Finally we assemble these ideas into a pseudo-spectral algorithm and demonstrate its efficiency on the Poisson equation. 相似文献
20.
On the jump behavior of distributions and logarithmic averages 总被引:1,自引:0,他引:1
Jasson Vindas Ricardo Estrada 《Journal of Mathematical Analysis and Applications》2008,347(2):597-606
The jump behavior and symmetric jump behavior of distributions are studied. We give several formulas for the jump of distributions in terms of logarithmic averages, this is done in terms of Cesàro-logarithmic means of decompositions of the Fourier transform and in terms of logarithmic radial and angular local asymptotic behaviors of harmonic conjugate functions. Application to Fourier series are analyzed. In particular, we give formulas for jumps of periodic distributions in terms of Cesàro–Riesz logarithmic means and Abel–Poisson logarithmic means of conjugate Fourier series. 相似文献