共查询到20条相似文献,搜索用时 31 毫秒
1.
The paper proves that, if f(x) ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in (-1, 1),then there exists a real rational function r(x) ∈ Rn^(2μ-1)l which is eopositive with f(x), such that the following Jackson type estimate ||f-r||p≤Cδl^2μωφ(f,1/n)p holds, where μ is a natural number ≥3/2+1/p, and Cδ is a positive constant depending only on δ. 相似文献
2.
Let B
p
n
={x∈\R
n
;\; \sum
i=1
n
|x
i
|
p
≤ 1} , 1≤ p\le+∈fty . We study the extreme values of the volume of the orthogonal projection of B
p
n
onto hyperplanes H\subset \R
n
. For a fixed H , we prove that the ratio vol(P
H
B
p
n
)/ vol(B
p
n-1
) is non-decreasing in p∈[1,+∈fty] .
Received May 21, 2001, and in revised form September 2, 2001. Online publication December 17, 2001. 相似文献
3.
We consider the best approximation of some function classes by the manifold M
n
consisting of sums of n arbitrary ridge functions. It is proved that the deviation of the Sobolev class W
p
r,d
from the manifold M
n
in the space L
q
for any 2≤ q≤ p≤∈fty behaves asymptotically as n
-r/(d-1)
. In particular, we obtain this asymptotic estimate for the uniform norm p=q=∈fty .
January 10, 2000. Date revised: March 1, 2001. Date accepted: March 12, 2001. 相似文献
4.
O. M. Fomenko 《Journal of Mathematical Sciences》2006,133(6):1733-1748
Let Sk(Γ) be the space of holomorphic Γ-cusp forms f(z) of even weight k ≥ 12 for Γ = SL(2, ℤ), and let Sk(Γ)+ be the set of all Hecke eigenforms from this space with the first Fourier coefficient af(1) = 1. For f ∈ Sk(Γ)+, consider the Hecke L-function L(s, f). Let
It is proved that for large K,
where ε > 0 is arbitrary. For f ∈ Sk(Γ)+, let L(s, sym
2 f) denote the symmetric square L-function. It is proved that as k → ∞ the frequence
converges to a distribution function G(x) at every point of continuity of the latter, and for the corresponding characteristic
function an explicit expression is obtained. Bibliography: 17 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 221–246. 相似文献
5.
A. V. Harutyunyan W. Lusky 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):128-135
Let U
n
be the unit polydisk in C
n
and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω
1, ..., ω
n
), ω
j
∈ S(1 ≤ j ≤ n) and f ∈ H(U
n
). The function f is said to be in holomorphic Besov space B
p
(ω) if
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
相似文献
6.
Marshall A. Whittlesey 《Arkiv f?r Matematik》1999,37(2):409-423
Let Δ be the closed unit disk in C, let Γ be the circle, let Π: Δ×C→Δ be projection, and letA(Δ) be the algebra of complex functions continuous on Δ and analytic in int Δ. LetK be a compact set in C2 such that Π(K)=Γ, and letK
λ≠{w∈C|(λ,w)∈K}. Suppose further that (a) for every λ∈Γ,K
λ is the union of two nonempty disjoint connected compact sets with connected complement, (b) there exists a function Q(λ,w)≠(w-R(λ))2-S(λ) quadratic in w withR,S∈A(Δ) such that for all λ∈Γ, {w∈C|Q(λ,w)=0}υ intK
λ, whereS has only one zero in int Δ, counting multiplicity, and (c) for every λ∈Γ, the map ω→Q(λ,ω) is injective on each component
ofK
λ. Then we prove that К/K is the union of analytic disks 2-sheeted over int Δ, where К is the polynomial convex hull ofK. Furthermore, we show that БК/K is the disjoint union of such disks. 相似文献
7.
Let r, k, s be three integers such that , or We prove the following:
Proposition.
Let Y:={y
i
}
i=1
s
be a fixed collection of distinct points y
i
∈ (-1,1) and Π (x):= (x-y
1
). ... .(x-y
s
). Let I:=[-1,1]. If f ∈ C
(r)
(I) and f'(x)Π(x) ≥ 0, x ∈ I, then for each integer n ≥ k+r-1 there is an algebraic polynomial P
n
=P
n
(x) of degree ≤ n such that P
n
'(x) Π (x) ≥ 0 and
$$ \vert f(x)-P_n(x) \vert \le B\left(\frac{1}{n^2}+\frac{1}{n}\sqrt{1-x^2}\right)^r \omega_k \left(f^{(r)};\frac{1}{n^2}+\frac{1}{n}\sqrt{1-x^2}\right)
\legno{(1)}$$
for all x∈ I, where ω
k
(f
(r)
;t) is the modulus of smoothness of the k -th order of the function f
(r)
and B is a constant depending only on r , k , and Y. If s=1, the constant B does not depend on Y except in the case
(r=1, k=3).
In addition it is shown that (1) does not hold for r=1, k>3.
March 20, 1995. Dates revised: March 11, 1996; December 20, 1996; and August 7, 1997. 相似文献
8.
Let Γ be the set of all permutations of the natural series and let α = {α j}
j∈ℕ, ν = {νj}
j∈ℕ, and η = {ηj}
j∈ℕ be nonnegative number sequences for which
9.
For any a,b∈R let ϕa,b(x)=ax+b(x∈R). Suppose 0<a<1. Let Ca,b be the generalized a-Cantor set with generating iterated function systme {ϕa,0, ϕa,b; ϕa,l}. Then we prove the Hausdorff dimension of Ca,c2 C_{a,c^2 } is \fracln(3 - ?5 - ln2lna\frac{{ln(3 - \sqrt 5 - ln2}}{{lna}} when 0<a≤2 cos 80°. 相似文献
10.
O. L. Vinogradov 《Journal of Mathematical Sciences》1998,92(1):3560-3572
Let C be the space of 2π-periodic continuous real functions with the uniform norm, let Hn be the set of trigonometric polynomials of order not more than n, let ω2(f) be the second continuity modulus for a function f∈C, and let Tn(f) be the best approximation polynomial of order n for f∈C. Set
; U:C→C;
. In this paper, for h sufficiently large we find the values C(U,h) for some positive operators U. For example, C(A0,h) and C(T0,h) are found. For n=1,2,3 we find the values
for some linear positive operators U:C→Hn. We establish relations between C(T0,h) and exact constants in the inequality ω2(f,h1)≤C(h1;h)ω2(f,h) for some h and h1 such that 0<h<h1≤π. For a seminorm P invariant with respect to the shift and majorized by the uniform norm, analogs of C(U,h) are estimated
from above. We investigate the problem of extension of a function defined on a segment with preservation of the second continuity
modulus. The relation
11.
Luca Brandolini Alex Iosevich Giancarlo Travaglini 《Journal of Fourier Analysis and Applications》2001,7(4):359-372
Let Γ be a smooth compact convex planar curve with arc length dm and let dσ=ψ dm where ψ is a cutoff function. For Θ∈SO (2)
set σΘ(E) = σ(ΘE) for any measurable planar set E. Then, for suitable functions f in ℝ2, the inequality.
12.
Horst Alzer 《Proceedings Mathematical Sciences》2010,120(2):131-137
Let n ≥ 1 be an integer and let P
n
be the class of polynomials P of degree at most n satisfying z
n
P(1/z) = P(z) for all z ∈ C. Moreover, let r be an integer with 1 ≤ r ≤ n. Then we have for all P ∈ P
n
:
|