共查询到8条相似文献,搜索用时 0 毫秒
1.
Sergei K. Suslov 《Journal of Approximation Theory》2002,115(2):289-353
We consider explicit expansions of some elementary and q-functions in basic Fourier series introduced recently by Bustoz and Suslov. Natural q-extensions of the Bernoulli and Euler polynomials, numbers, and the Riemann zeta function are discussed as a by-product. 相似文献
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V. A. Abilov F. V. Abilova M. K. Kerimov 《Computational Mathematics and Mathematical Physics》2009,49(6):927-941
Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space L 2((a, b), p(x)). Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered. 相似文献
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《Applied and Computational Harmonic Analysis》2014,36(3):387-415
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that using generalized sampling one obtains a stable and accurate reconstruction, provided the number of Fourier samples grows linearly in the number of wavelet coefficients recovered. For the class of Daubechies wavelets we derive the exact constant of proportionality.Our second result concerns the optimality of generalized sampling for this problem. Under some mild assumptions we show that generalized sampling cannot be outperformed in terms of approximation quality by more than a constant factor. Moreover, for the class of so-called perfect methods, any attempt to lower the sampling ratio below a certain critical threshold necessarily results in exponential ill-conditioning. Thus generalized sampling provides a nearly-optimal solution to this problem. 相似文献
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S. S. Volosivets 《Mathematical Notes》2006,80(5-6):663-672
In this paper, we prove direct and inverse theorems of approximation theory in the space of p-absolutely continuous functions which generalize Terekhin’s results in the same way as Timan’s results in L p generalize the classical theorems of approximation theory. The main theorems are refined for functions with quasimonotone Fourier coefficients and, in a number of cases, the resulats are shown to be sharp. 相似文献
6.
Myriam Codes María Laura Delgado Martín María Consuelo Monterrubio Pérez 《International Journal of Mathematical Education in Science & Technology》2013,44(5):652-662
In this paper, we describe the growth of mathematical understanding in university students engaged in mathematics classroom tasks regarding the concept of numerical series. Starting from the Image-Making Pirie and Kieren theory layer, students organize a mathematical concept linking different mathematical elements. In this process, there are important agents that are involved during the interactions to advance in this construction through the mechanism of folding back between different layers. 相似文献
7.
Some Recent Developments in the Theory and Applications of a Class of Finite Fourier Transformations
H. M. Srivastava 《Numerical Functional Analysis & Optimization》2013,34(1-2):295-306
In this talk we shall investigate various properties of a class of finite Fourier transformations (that is, Fourier transformations on finite intervals), not as Fourier coefficients, but as functions of a continuous variable. Some of these potentially useful properties of finite Fourier exponential, finite Fourier sine, and finite Fourier cosine transformations will then be applied to several families of special functions including (for example) Bessel functions, parabolic cylinder functions, and Chebyshev and Legendre (or spherical) polynomials. 相似文献