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41.
Josef Obermaier 《Journal of Approximation Theory》2003,125(2):303-312
Let
be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (Pn)n=0∞ with deg Pn=n such that every fC(S) has a unique representation f=∑i=0∞ αiPi and call such a basis Faber basis. In the special case of
, 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(Sq)≠U(Sq)=C(Sq), where A(Sq) is the so-called Wiener algebra and U(Sq) is the set of all fC(Sq) which are uniquely represented by its Fourier series. 相似文献
42.
In this paper, we present a new algorithm to estimate a regression function in a fixed design regression model, by piecewise
(standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees
of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances
of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain
how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty
term is chosen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known
or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising
and of compression. 相似文献
43.
44.
45.
Kung-Yu Chen 《Journal of Mathematical Analysis and Applications》2004,298(2):411-417
In his recent investigations involving differential operators for some generalizations of the classical Laguerre polynomials, H. Bavinck [J. Phys. A Math. Gen. 29 (1996) L277-L279] encountered and proved a certain summation identity for the classical Laguerre polynomials. The main object of this sequel to Bavinck's work is to prove a generalization of this summation identity for the Srivastava-Singhal polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. It is also indicated how the general summation identity can be applied to derive the corresponding result for one class of the Konhauser biorthogonal polynomials. 相似文献
46.
利用第一类Chebyshev多项式的性质以及其与Lucas数的关系得到了关于Lucas数立方的一些恒等式. 相似文献
47.
Shy-Der Lin 《Journal of Mathematical Analysis and Applications》2004,294(2):399-411
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated single-, double-, and triple-integral representations. Some known or new consequences of the general results presented here, involving such classical orthogonal polynomials as the Jacobi, Laguerre, Hermite, and Bessel polynomials, and various other relatively less familiar hypergeometric polynomials, are also considered. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. 相似文献
48.
关于一个数论函数的导数及应用 总被引:1,自引:0,他引:1
Kanemitsu教授给出了欧拉求和函数的推广公式Lu(x,a)=0n相似文献
49.
Bourget Alain Jakobson Dmitry Min-Oo Maung Toth John A. 《Letters in Mathematical Physics》2003,64(2):105-118
We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes. 相似文献
50.
关于正形置换多项式的注记 总被引:5,自引:1,他引:4
n为正整数,m为大于1的正整数,本文证明了当n≡0,1(mod m)时,F2^n上不存在2^m-1次正形置换多项式,并给出了该结果的几个推论:F2^n上不存在次数为3的正形置换多项式;n〉2时,F2^n上的4次正形置换多项式都是仿射多项式. 相似文献