R. Hunt, On the convergence of Fourier series. in Orthogonal Expansions and their Contin- uous Analogues (Proc. Conf., Edwardsville, Ill.,) (1967), 235{255, Southern Illinois Univ. Press, Carbondale, Ill.R. A. Hunt. On the convergence of Fourier series. Orthogonal Expansions and their ...
The rate of convergence of a Fourierseries representation of a given function depends on the nature of the function and of its derivatives. This is shown by using the graphical outputs of a desk computer for different cases. For fullrange series, the effects of continuity and discontinuity of ...
Do, Y.Q., Lacey, M.T.: On the convergence of lacunary Walsh–Fourier series. Bull. Lond. Math. Soc. 44 (2), 241–254 (2012). : 10.1112/blms/bdr088Yen Q. Do and Michael T. Lacey. On the convergence of lacunary Walsh-Fourier series. Bull. Lond. Math. Soc., 44(2):241-254...
On the Convergence of Lacunary Walsh-Fourier Series We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the s... YQ Do,MT Lacey - 《Bulletin of the London Mathematical Society》 被引量:...
On the uniform convergence of Fourier Series 来自 Semantic Scholar 喜欢 0 阅读量: 6 作者: A Rakhimov 摘要: We prove theorems on the uniform summabilty of Fourier-Laplace series of distributions from the Sobolev spaces with negative smoothness defined on a unique sphere. 年份: 2016 ...
bn ∫_(-π)^xf(t)dt=(a_0(π+x))/2+∑_(n=1)^∞[(a_n)/nsinnx-(b_n)/n)(cosnx-cosn ] n n=1 Putting x = 0, we get ∫_(-π)^0f(t)dt=(a_0π)/2-∑_(n=0)^∞(b_n)/n|1-(-1)^n1^n n=1 This implies convergence of the series Zn=1(bn/n)[1-(-1)"...
{R}.$ Using obtained representation we investigate the problems of convergence in the spaces $L_p(\mathbb{R}),~ p> 1,$ and pointwise convergence of Fourier series on the systems $\{\Phi_n(t)\},~ n \in \mathbb{Z},$ provided that the sequences of poles of these systems satisfies...
In the present paper, the random series ∑ m = 0 ∞ c m C m ( ) q ( ζ , η ) m ( u ) \sum\limits_{m=0}^\infty c_m C_m(\varpi)q_m^{(\zeta,\eta)}(u) in orthogonal Jacobi polynomials q ( ζ , η ) m ( u ) q_m^{(\zeta,\eta)}(u) is discussed. The ...
On convergence and growth of partial sums of Fourier series. Acta Math. 116, 135–157 (1966). https://doi.org/10.1007/BF02392815 Download citation Received31 January 1966 Issue DateDecember 1966 DOIhttps://doi.org/10.1007/BF02392815 Keywords Fourier Fourier Series Access this article Log in ...
In this paper the absolute convergence of the Fourier series is studied for the class of the function f with the modulus of continuity and the modulus of variation satif ying the conditions ω(δ, f) = O(ω(δ)) and v(n, f) = 0(v(n)) respectively, where the modulus of continuity...