共查询到20条相似文献，搜索用时 31 毫秒
1.
A. V. Filinovskii 《Mathematical Notes》1997,61(5):635-643
The following boundary value problem is studied:
here the surface Г satisfies the condition(
, where
and ν is the outward (with respect to Ω) normal to Γ.
Translated fromMatematischskie Zametki, Vol. 61, No. 5, pp. 759–768, May, 1997.
Translated by N. K. Kulman 相似文献
2.
For multiplicative functions ƒ(n), let the following conditions be satisfied: ƒ(n)≥0 ƒ(p
r)≤A
r,A>0, and for anyε>0 there exist constants
,α>0 such that
and Σ
p≤x
ƒ(p) lnp≥αx. For such functions, the following relation is proved:
. Hereτ(n) is the number of divisors ofn andC(ƒ) is a constant.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 443–456, September, 1998.
The work of the first author was supported by the Russian Foundation for Basic Research. 相似文献
3.
L. G. Arabadzhyan 《Mathematical Notes》1997,62(3):271-277
We study the solvability of the integral equation
, wheref∈L
1
loc(ℝ) is the unknown function andg,T
1, andT
2 are given functions satisfying the conditions
.
Most attention is paid to the nontrivial solvability of the homogeneous equation
.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 323–331, September, 1997.
Translated by M. A. Shishkova 相似文献
4.
Wang Lei Pan Ting Dept. of Math. Zhejiang Univ. Hangzhou China. Univ. of International Relation Hangzhou China. 《高校应用数学学报(英文版)》2004,19(2):212-222
Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1 01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(… 相似文献
5.
L. V. Kritskov 《Mathematical Notes》1999,65(4):454-461
Suppose thatА is a nonnegative self-adjoint extension to {
} of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {
} or the condition {
} in which the nonnegative function itχ(r) is such that {
}. For each α∈(0, 2], we establish an estimate of the generalized Fourier transforms of an arbitrary function {
} of the form {
} If, in addition, {
}, then, along with this estimate, a similar lower bound is established.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 542–551, April, 1999. 相似文献
6.
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
7.
§ 1 IntroductionIn this note we are concerned with the asymptotically periodic second order equation-u″+α( x) u =β( x) uq +γ( x) up, x∈ R,( 1 )where1 相似文献
8.
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
9.
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
10.
O. I. Kuznetsova 《Mathematical Notes》1998,63(3):352-356
An analog of Fomin's well-known one-dimensional theorem is proved for trigonometric series of the form
given on anN-dimensional torus, whereV is some polyhedron in ℝ{upN}.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 402–406, March, 1998. 相似文献
11.
A. I. Zvyagintsev 《Mathematical Notes》1997,62(5):596-606
For functions satisfying the boundary conditions
, the following inequality with sharp constants in additive form is proved:
wheren≥2, 0≤1≤n−2,−1≤m≤1, m+1≤n−3, and1≤p,q,r≤∞.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 712–724, November, 1997.
Translated by N. K. Kulman 相似文献
12.
Fa-en WU~ 《中国科学A辑(英文版)》2007,50(8):1078-1086
Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 ＜ λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang. 相似文献
13.
Liu Yuji 《Mathematica Slovaca》2007,57(3):225-242
In this paper, we establish sufficient conditions to guarantee the existence of at least three or 2n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian
and one of following boundary conditions
and
Examples are presented to illustrate the main results.
Supported by National Natural Science Foundation of P. R. China (No: 10371006). 相似文献
| ((1)) |
| ((2)) |
| ((3)) |
14.
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
15.
S. Ya. Khavinson 《Mathematical Notes》1999,65(5):620-626
Suppose thatG is a finitely connected domain with rectifiable boundary γ, ∞εG, the domainsD
1,...,D
s
are the complements ofG, the subsetsF
j
⊂D
j
are infinite and compact,n
j
≥1,j=1,...,s, are integers, λ0 is a complex-valued measure on γ, and
We consider the extremum problem
where μ
j
,j=1,...,s, are complex-valued measures onF
j
and
are Golubev sums. We prove that β=Δ, where
We also establish several other relations between these and other extremal variables.
Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 738–745, May, 1999. 相似文献
16.
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
17.
V. N. Grishin 《Mathematical Notes》1999,66(5):533-540
A set-theoretic LST system based on a logic without rules of contraction of identical formulas in the antecedent or succedent
of sequents is introduced. The set-theoretic axioms used are the comprehension principle,
, where the weight of the variablex in the formulaA(x) is at most one (see below), and the extensionality principle,
.
It is proved that the restriction on the weight of the variablex in the comprehension axiom is essential. Examples of comprehension axioms with the weight of variablex equal to 2 whose combination with the extensionality principle leads to a contradiction in the logic without contraction
rules are constructed.
Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 643–652, November, 1999. 相似文献
18.
P. Ding 《Journal of Mathematical Sciences》2006,137(2):4645-4653
Let p be a prime number, n be a positive integer, and ƒ(x) = axk + bx. We put
where e(t) = exp(2πit). This special exponential sum has been widely studied in connection with Waring’s problem. We write n in the form n
= Qk + r, where 0 ≤ r ≤ k − 1 and Q ≥ 0. Let α = ord
p(k), β = ord
p(k − 1), and θ = ord
p(b). We define
and J = [ζ]. Moreover, we denote V = min(Q, J). Improving the preceding result, we establish the theorem. Theorem. Let k ≥ 2 and n ≥ 2. If p > 2, then
. An example showing that this result is best possible is given. Bibliography: 15 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 63–75. 相似文献
19.
WANGSHU WENSHIHLIANG YEQIXIAO 《高校应用数学学报(英文版)》1997,12(2):127-138
ＦＩＮＩＴＥＴＲＡＶＥＬＩＮＧＷＡＶＥＳＦＯＲＡＲＥＡＣＴＩＯＮ┐ＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭＷＩＴＨＮ（３）ＣＯＭＰＯＮＥＮＴＳＷＡＮＧＳＨＵ,ＷＥＮＳＨＩＨＬＩＡＮＧＡＮＤＹＥＱＩＸＩＡＯＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｅｘ... 相似文献
20.
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
, where
, for some ε > 0, then f ≡ 0. We construct a (p,A)-lacunary series f
0 such that
with a constant C0 = C0(p,A) > 0. Bibliography: 4 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2003, pp. 135–149. 相似文献