共查询到20条相似文献,搜索用时 31 毫秒
1.
Let Bσ,p,1 <-p<-∞, be the set of all functions from L8(R) which can be continued to entire functions of exponential type <-σ. The well known Shannon sampling theorem and its generalization [1] state that every f∈Bσ,p, 1
$$f(x) = \mathop \Sigma \limits_{j \in z} f(j\pi /\sigma )\tfrac{{sin\sigma (x - j\pi /\sigma )}}{{\sigma (x - j\pi /\sigma )}}, \sigma > 0$$ It is well known that the Shannon sampling theorem plays an important role in many applied fields [1,2,7]. In this paper we give an application of sampling theorem to approximation theory. 相似文献
2.
K. Tandori 《Analysis Mathematica》1979,5(2):149-166
Пусть {λ n 1 t8 — монотонн ая последовательнос ть натуральных чисел. Дл я каждой функции fεL(0, 2π) с рядом Фурье строятся обобщенные средние Bалле Пуссена $$V_n^{(\lambda )} (f;x) = \frac{{a_0 }}{2} + \mathop \sum \limits_{k = 1}^n (a_k \cos kx + b_k \sin kx) + \mathop \sum \limits_{k = n + 1}^{n + \lambda _n } \left( {1 - \frac{{k - n}}{{\lambda _n + 1}}} \right)\left( {a_k \cos kx + b_k \sin kx} \right).$$ Доказываются следую щие теоремы.
- Если λn=o(n), то существуе т функция fεL(0, 2π), для кот орой последовательность {Vn (λ)(?;x)} расходится почти вс юду.
- Если λn=o(n), то существуе т функция fεL(0, 2π), для кот орой последовательность $$\left\{ {\frac{1}{\pi }\mathop \smallint \limits_{ - \pi /\lambda _n }^{\pi /\lambda _n } f(x + t)\frac{{\sin (n + \tfrac{1}{2})t}}{{2\sin \tfrac{1}{2}t}}dt} \right\}$$ расходится почти всю ду
3.
Получены асимптотич еские равенства для в еличин гдеr≧0 — целое, ω(t) — выпу клый модуль непрерыв ности и $$\bar \sigma _n (f;x) = - \frac{1}{\pi } \mathop \smallint \limits_{ - \pi }^\pi f(x + t)\left( {\frac{1}{2}ctg\frac{t}{2} - \frac{1}{{4(n + 1)}}\frac{{\sin (n + 1)t}}{{\sin ^2 \tfrac{1}{2}t}}} \right)dt$$ сумма Фейера функцииf(х), сопряженной сf(x). 相似文献
4.
Let μ be a measure with compact support, with orthonormal polynomials {p
n
} and associated reproducing kernels {K
n
}. We show that bulk universality holds in measure in {ξ: μ′(ξ) > 0}. More precisely, given ɛ, r > 0, the linear Lebesgue measure of the set {ξ: μ′(ξ) > 0} and for which
$\mathop {\sup }\limits_{\left| u \right|,\left| v \right| \leqslant r} \left| {\frac{{K_n (\xi + u/\tilde K_n (\xi ,\xi ),\xi + v/\tilde K_n (\xi ,\xi ))}}
{{K_n (\xi ,\xi )}}} \right. - \left. {\frac{{\sin \pi (u - v)}}
{{\pi (u - v)}}} \right| \geqslant \varepsilon$\mathop {\sup }\limits_{\left| u \right|,\left| v \right| \leqslant r} \left| {\frac{{K_n (\xi + u/\tilde K_n (\xi ,\xi ),\xi + v/\tilde K_n (\xi ,\xi ))}}
{{K_n (\xi ,\xi )}}} \right. - \left. {\frac{{\sin \pi (u - v)}}
{{\pi (u - v)}}} \right| \geqslant \varepsilon 相似文献
5.
Achiya Dax 《BIT Numerical Mathematics》1997,37(3):600-622
This paper presents a proximal point algorithm for solving discretel
∞ approximation problems of the form minimize ∥Ax−b∥∞. Let ε∞ be a preassigned positive constant and let ε
l
,l = 0,1,2,... be a sequence of positive real numbers such that 0 < ε
l
< ε∞. Then, starting from an arbitrary pointz
0, the proposed method generates a sequence of points z
l
,l= 0,1,2,..., via the rule
. One feature that characterizes this algorithm is its finite termination property. That is, a solution is reached within
a finite number of iterations. The smaller are the numbers ε
l
the smaller is the number of iterations. In fact, if ε
0
is sufficiently small then z1 solves the original minimax problem.
The practical value of the proposed iteration depends on the availability of an efficient code for solving a regularized minimax
problem of the form minimize
where ∈ is a given positive constant. It is shown that the dual of this problem has the form maximize
, and ify solves the dual thenx=A
T
y solves the primal. The simple structure of the dual enables us to apply a wide range of methods. In this paper we design
and analyze a row relaxation method which is suitable for solving large sparse problems. Numerical experiments illustrate
the feasibility of our ideas. 相似文献
6.
M. N. Sheremeta 《Mathematical Notes》1998,63(3):401-410
For the Dirichlet series corresponding to a functionF with positive exponents increasing to ∞ and with abscissa of absolute convergenceA ∈ (−∞, +∞], it is proved that the sequences (μ(σ, F
(m)
)) of maximal terms and (Λ(σ, F
(m)
)) of central exponents are nondecreasing to ∞ asm → ∞ for any givenσ <A, and
7.
A power series
with radius of convergence equal 1 is called a (p,A)-lacunary one if nk ≥ Akp, A > 0, 1 < p < ∞. It is proved that if 1 < p < 2 and f(x) is a (p,A)-lacunary series that satisfies the condition
8.
Winfried Sickel 《Constructive Approximation》1992,8(3):257-274
Let
|