共查询到20条相似文献,搜索用时 78 毫秒
1.
O. L. Vinogradov 《Journal of Mathematical Sciences》1999,97(4):4233-4237
Let C be the space of 2π-periodic continuous real-valued functions, let
be first- and second-order moduli of continuity of a function f∈C with step h≥0. Denote by Lip1 = {f ∈ C: ω1(f,h) = O(h)} the Lipschitz class and by Z1 = {f ∈ C: ω2(f,h) = O(h)} the Zygmund class. The class of functions W⊂C is said to be described in terms of the kth modulus of continuity
if for any functions f1, f2∈C such that ωk(f2) from f1∈W it follows that f2∈W. As is shown, the class Z1 is not described in terms of the first-order modulus of continuity, whereas the class Lip is not described in terms of the
second-order modulus of continuity. Bibliography: 3 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 83–89. 相似文献
2.
F. Luca 《Lithuanian Mathematical Journal》2007,47(3):243-247
Let p
n
be the nth prime. In this note, we show that the set of n such that
is a square is of asymptotic density zero.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 301–306, July–September, 2007. 相似文献
3.
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
4.
O. M. Fomenko 《Journal of Mathematical Sciences》2008,150(3):2115-2122
For a cubic extension K3/ℚ, which is not normal, new results on the behavior of mean values of the Dedekind zeta function of the field K3 in the critical strip are obtained.
Let M(m) denote the number of integral ideals of the field K3 of norm m. For the sums
asymptotic formulas are derived. Previously, only upper bounds for these sums were known. Bibliography: 23 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 350, 2007, pp. 187–198. 相似文献
5.
O. M. Mulyava 《Ukrainian Mathematical Journal》2006,58(9):1441-1447
Under certain conditions on continuous functions μ, λ, a, and f, we prove the inequality
and describe its application to the investigation of the problem of finding conditions under which Laplace integrals belong
to a class of convergence.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1271–1275, September, 2006. 相似文献
6.
N. A. Shirokov 《Journal of Mathematical Sciences》2006,134(4):2320-2323
Let Λα be the analytic Holder class in the unit disk
. For f ∈ Λα and
, let Mf (I) = max
I |f|. Assume that I and J are arcs such that |J| = 2|I| and J and I have the same midpoint. Then
It is proved that this estimate cannot be improved. Bibliography: 1 title.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 315, 2004, pp. 149–154. 相似文献
7.
Ryoichi Shimizu 《Annals of the Institute of Statistical Mathematics》1986,38(1):195-204
Summary LetX be a positive random variable with the survival function
and the densityf. LetX have the moments μ=E(X) and μ2=E(X
2) and put ε=|1-μ2/2μ2|. Put
and
. It is proved that the following inequalities hold:
, for allx>0, ifq(x) is monotone and that
, ifq
1
(x) is monotone. It is also shown that Brown's inequality
which holds wheneverq
1
(x) is increasing is not valid in general whenq
1 is decreasing.
The Institute of Statistical Mathematics 相似文献
8.
Let {zk=xk+iyk} be a sequence on upper half plane
and {si} be the number of appearence of zk in {z1,z2,...,zk}. Suppose sup si<+∞. Let ω(x) be a weight belonging to A∞ and
. We Consider the weighted Hardy space
and operator Tp mapping f(z)∈H
+w
p
into a sequence defined by
, 0<p≤+∞, j=1,2,.... Then Tp(H
+w
p
)=lp if and only if {zk} is uniformly separated. Besides the effective solution for interpolation is obtained.
Supported by National Science Foundation of China and Shanghai Youth Science Foundation 相似文献
9.
Let p be an odd prime and let δ be a fixed real number with 0<δ<2. For an integer a with 0<a<p, denote by ā the unique integer between 0 and p satisfying a
ā≡1 (mod p). Further, let {x} denote the fractional part of x. We derive an asymptotic formula for the number of pairs of integers (a, b with
.
This work is supported by N. S. F. of P. R. China (10271093) 相似文献
10.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献
11.
Bogdan Batko Jacek Tabor 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):67-73
Let G be a commutative semigroup and letL be a complete Archimedean Riesz Space. Suppose thatF: G → L satisfies for somee ∈ L
+ the inequality
Then there exists a unique additive mappingA : G → L such that
As the method of the proof we use the Johnson-Kist Representation Theorem. 相似文献
12.
Abstract
With Littlewood–Paley analysis, Peetre and Triebel
classified, systematically, almost all the usual function spaces
into two classes of spaces: Besov spaces
and Triebel–Lizorkin
spaces
; but the structure of
dual spaces
of
is very different from
that of Besov spaces or that of Triebel–Lizorkin spaces, and
their structure cannot be analysed easily in the
Littlewood–Paley analysis. Our main goal is to characterize
in tent spaces with
wavelets. By the way, some applications are given: (i)
Triebel–Lizorkin spaces for p
= ∞ defined by Littlewood–Paley analysis cannot serve as the dual
spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations
among these above spaces and some relations among
and
L
1
are studied.
Supported by NNSF of China (Grant No.
10001027) 相似文献
13.
A nontrivial product in the stable homotopy groups of spheres 总被引:13,自引:0,他引:13
LIU XiuguiInstitute of Mathematics Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2004,47(6):831-841
Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Li-uleviciusdescribed hi and bk in Ext (A|*,*) (Zp, Zp) having bigrading (1,2pi(p-1))and (2,2pk+1 x(p - 1)), respectively. In this paper we prove that for p ≥ 7,n ≥ 4 and 3 ≤ s < p - 1, (Zp,Zp) survives to E∞ in the Adams spectral sequence, where q = 2(p - 1). 相似文献
14.
We prove a general theorem on the zeros of a class of generalised Dirichlet series. We quote the following results as samples.
Theorem A.Let 0<θ<1/2and let {a
n
}be a sequence of complex numbers satisfying the inequality
for N = 1,2,3,…,also for n = 1,2,3,…let α
n
be real and |αn| ≤ C(θ)where C(θ) > 0is a certain (small)constant depending only on θ. Then the number of zeros of the function
in the rectangle (1/2-δ⩽σ⩽1/2+δ,T⩽t⩽2T) (where 0<δ<1/2)is ≥C(θ,δ)T logT where C(θ,δ)is a positive constant independent of T provided T ≥T
0(θ,δ)a large positive constant.
Theorem B.In the above theorem we can relax the condition on a
n
to
and |aN| ≤ (1/2-θ)-1.Then the lower bound for the number of zeros in (σ⩾1/3−δ,T⩽t⩽2T)is > C(θ,δ) Tlog T(log logT)-1.The upper bound for the number of zeros in σ⩾1/3+δ,T⩽t⩽2T) isO(T)provided
for every ε > 0.
Dedicated to the memory of Professor K G Ramanathan 相似文献
15.
In this paper, a natural R
+
n+1
extension of singular integrals, i.e.,T
κ:f→K*φ
t
*t with K a standard C-Z kernel and ϕ usual one, is investigated. One of the main results is: Let (dμ, udx) ∈C1 and u-Mw, w∈A∞, then Tk is of type (Lp(udx), Lp(dμ)). As a related topic, a maximal operator
is proved to be of type
, where
, provided (dμ, udx) ∈C1 and u∈ A∞.
Supported by National Science Foundation of China 相似文献
16.
17.
O. M. Fomenko 《Journal of Mathematical Sciences》2007,143(3):3174-3181
Let f(z) be a holomorphic Hecke eigencuspform of even weight k with respect to SL(2, Z) and let L(s, sym
2 f) = ∑
n=1
∞
cnn−s, Re s > 1, be the symmetric square L-function associated with f.
Represent the Riesz mean (ρ ≥ 0)
as the sum of the “residue function” Γ(ρ+1)−1 Ł(0, sym2f)xρ and the “error term”
.
Using the Voronoi formula for Δρ(x;sym
2f), obtained earlier (see Zap. Nauchn. Semin. POMI. 314, 247–256 (2004)), the integral
is estimated. In this way, an asymptotics for 0 < ρ ≤ 1 and an upper bound for ρ = 0 are obtained. Also the existence of
a limiting distribution for the function
, and, as a corollary, for the function
, is established. Bibliography: 12 titles.
Dedicated to the 100th anniversary of G. M. Goluzin’s birthday
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 274–286. 相似文献
18.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
19.
Michela Eleuteri 《Applications of Mathematics》2007,52(2):137-170
We prove some optimal regularity results for minimizers of the integral functional ∫ f(x, u, Du) dx belonging to the class K ≔ {u ∈ W
1,p
(Ω): u ⩾ ψ, where ψ is a fixed function, under standard growth conditions of p-type, i.e.
.
This research has been supported by INdAM.
On leave from: Dipartimento di Matematica, Universitá di Trento, via Sommarive 14, 38050 Povo (Trento), Italy, e-mail: eleuteri@science.unitn.it. 相似文献
20.
Let f(x, y) be a periodic function defined on the region D
with period 2π for each variable. If f(x, y) ∈ C
p (D), i.e., f(x, y) has continuous partial derivatives of order p on D, then we denote by ω
α,β(ρ) the modulus of continuity of the function
and write
For p = 0, we write simply C(D) and ω(ρ) instead of C
0(D) and ω
0(ρ).
Let T(x,y) be a trigonometrical polynomial written in the complex form
We consider R = max(m
2 + n
2)1/2 as the degree of T(x, y), and write T
R(x, y) for the trigonometrical polynomial of degree ⩾ R.
Our main purpose is to find the trigonometrical polynomial T
R(x, y) for a given f(x, y) of a certain class of functions such that
attains the same order of accuracy as the best approximation of f(x, y).
Let the Fourier series of f(x, y) ∈ C(D) be
and let
Our results are as follows
Theorem 1 Let f(x, y) ∈ C
p(D (p = 0, 1) and
Then
holds uniformly on D.
If we consider the circular mean of the Riesz sum S
R
δ
(x, y) ≡ S
R
δ
(x, y; f):
then we have the following
Theorem 2 If f(x, y) ∈ C
p (D) and ω
p(ρ) = O(ρ
α (0 < α ⩾ 1; p = 0, 1), then
holds uniformly on D, where λ
0
is a positive root of the Bessel function J
0(x)
It should be noted that either
or
implies that f(x, y) ≡ const.
Now we consider the following trigonometrical polynomial
Then we have
Theorem 3 If f(x, y) ∈ C
p(D), then uniformly on D,
Theorems 1 and 2 include the results of Chandrasekharan and Minakshisundarm, and Theorem 3 is a generalization of a theorem
of Zygmund, which can be extended to the multiple case as follows
Theorem 3′ Let f(x
1, ..., x
n) ≡ f(P) ∈ C
p
and let
where
and
being the Fourier coefficients of f(P). Then
holds uniformly.
__________
Translated from Acta Scientiarum Naturalium Universitatis Pekinensis, 1956, (4): 411–428 by PENG Lizhong. 相似文献