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1.
Mats Andersson 《Journal d'Analyse Mathématique》1996,68(1):39-58
LetG
1,…,Gm be bounded holomorphic functions in a strictly pseudoconvex domainD such that
. We prove that for each
(0,q)-form ϕ inL
p(∂D), 1<p<∞, there are
formsu
1, …,u
m inL
p(∂D) such that ΣG
juj=ϕ. This generalizes previous results forq=0. The proof consists in delicate estimates of integral representation formulas of solutions and relies on a certainT1 theorem due to Christ and Journé. For (0,n−1)-forms there is a simpler proof that also gives the result forp=∞. Restricted to one variable this is precisely the corona theorem.
The author was partially supported by the Swedish Natural Research Council. 相似文献
2.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
3.
On the uniform strong approximation of Marcinkiewicz type for multivariable continuous functions 总被引:2,自引:0,他引:2
Yujun Zhang Xiaoyuan He 《分析论及其应用》2005,21(4):377-384
The rate of uniform strong approximation of Marcinkiewicz type for multivariable continuous func-tions is obtained in this paper as follows:‖1/k 1 k∑j=0|Sj(f)- f|q‖≤C/k 1 k∑j=0 Eqj(f),where Sj (f) denotes the square partial Fourier sum of f and Ej (f) denotes the square best approximation of f by trigonometric polynomials of degree (j, j, … ,j),j = 0,1, 2,…. 相似文献
4.
Let
be a set of finite groups. A group G is saturated with groups from
if every finite subgroup of G is contained in a subgroup isomorphic to some member of
. It is proved that a periodic group G saturated with groups from the set {L3(2m)|m = 1, 2, …} is isomorphic to L3(Q), for a locally finite field Q of characteristic 2; in particular, it is locally finite.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 606–626, September–October, 2007. 相似文献
5.
D. M. Smirnov 《Algebra and Logic》2005,44(5):348-352
We deal with varieties with one basic operation f(x1,...,xn) and one defining identity f(x1,..., xn) = f(xπ(1),...,xπ(n)), where π is a permutation whose cyclic set consists of distinct primes p1,...,pr, with the sum p1+...+pr = n. Their interpretability types, together with the greatest element 1 in a lattice
int, are said to be arithmetic. It is proved that the arithmetic types constitute a distributive lattice
ar, which is dual to a lattice Sub
fΠ of finite subsets of the set Π of all primes. It is shown that for n ⩾ 2, the poset
ar(
n) of arithmetic types defined by permutations in
n, for n fixed, is a lattice iff n = 2, 3, 4, 6, 8, 9, 11.
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Translated from Algebra i Logika, Vol. 44, No. 5, pp. 622–630, September–October, 2005. 相似文献
6.
Research on finite solvable groups with C-closed invariant subgroups has given rise to groups structured as follows. Let p,
q1, q2, ..., qm be distinct primes, ni be the exponent of p modulo qi, and n be the exponent of p modulo
. Then G = Pλ〈x〉, where P is a group and
; Zi; here, Zi and P/Z(P) are elementary Abelian groups of respective orders
and pn, |x| = r, the element x acts irreducibly on P/Z(P) and on each of the subgroups Zi, and
. We state necessary and sufficient conditions for such groups to exist.
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Translated from Algebra i Logika, Vol. 45, No. 4, pp. 379–389, July–August, 2006. 相似文献
7.
Some remarks on trigonometric sums 总被引:1,自引:1,他引:0
Let
where m
1 < m
2 < … < m
t
≦ , δ
x
→ 0, p runs over the primes p ≧ ≦ 1, |X
p
| ≦ 1. It is assumed that m
v
, , X
p
may depend on x.
Assume that . It is proved that
for almost all irrational α, π(x) = number of primes up to x.
Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA
T46993. 相似文献
8.
WangJianli ZhouSongping 《分析论及其应用》2003,19(3):280-288
The present paper deals with best onesided approximation rate in Lp spaces ^~En(f)Lp of f∈C2π.Although it is clear that the estimate ^~E(f)Lp≤C‖f‖Lp cannot be correct for all f∈L^p2π in case p<∞, the question whether ~En(f)Lp≤Cω(f,n^-l)Lp or ^~En(f)Lp≤CEn(f)Lp holds for f∈ C2π remains totally untouched.Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis. 相似文献
9.
V. P. Burichenko 《Algebra and Logic》2000,39(3):160-183
We study groups
. which are nonsplit extensions of elementary Abelian 2-groups A by H ∼ L2(q), with H acting on A irreducibly and A ≠ Z2. Related cohomology groups are computed. Groups
are given a complete regimentation for odd q. Moreover, there is only one, up to isomorphism, group
for q ≡ −1 (mod 4) and there is none for q ≡ 1 (mod 4). We also present an explicit construction of
treated as automorphism groups of some loops close to extraspecial groups, the so-called “code loops” brought in sight by
Griess and Parker.
Supported by Byelorus Republican Foundation for Fundamental Research grant No. F97M-02.
Translated fromAlgebra i Logika, Vol. 39, No. 3, pp. 280–319, May–June, 2000. 相似文献
10.
A. S. Fedorenko 《Ukrainian Mathematical Journal》2000,52(6):981-986
We consider the approximation of functions of the classes of
by Zygmund sums. In papticular, we present asymptotic equalities for the quantities
under various conditions imposed on functions ψ1(·) and ψ2(·).
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52,
No. 6, pp. 856–860, June, 2000. 相似文献
11.
A graphG is embeddable in its complement
ifG is isomorphic with a subgraph of
. A complete characterization is given of those (p,p−1) graphs which are embeddable in their complements. In particular, letG be a (p,p−1) graph wherep≧6 ifp is even andp≧9 ifp is odd; thenG is embeddable in
if and only ifG is neither the starK
1,p−1 norK
1,n
∪C
3 withn≧4. 相似文献
12.
We introduce a notion which is intermediate between that of taking thew*-closed convex hull of a set and taking the norm closed convex hull of this set. This notion helps to streamline the proof
(given in [FLP]) of the famous result of James in the separable case. More importantly, it leads to stronger results in the
same direction. For example:
相似文献
1. | AssumeX is separable and non-reflexive and its unit sphere is covered by a sequence of balls of radiusa<1. Then for every sequence of positive numbers tending to 0 there is anf εX*, such that ‖f‖ = 1 andf (x)≤1 −ε i , wheneverx εC i ,i=1,2,… |
2. | AssumeX is separable and non-reflexive and letT:Y →X* be a bounded linear non-surjective operator. Then there is anf εX* which does not attain its norm onB X such thatf ∉T(Y). |
13.
If w1,…,w
N is a finite sequence of nonzero points in the unit disk, then there are distinct points λ1,…, λN on the unit circle and positive numbers Μ1,…,Μ
N such that
is the zero sequence of the function 1 —
. The points λ1,…, λN and numbers Μ1,…,ΜN are unique (except for reorderings). 相似文献
14.
It is proved that an irreducible quasifinite
-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight
-module is a module of the intermediate series. For a nondegenerate additive subgroup Λ ofF
n, whereF is a field of characteristic zero, there is a simple Lie or associative algebraW(Λ,n)(1) spanned by differential operatorsuD
1
m
…D
1
m
foru ∈F[Γ] (the group algebra), andm
i≥0 with
, whereD
i are degree operators. It is also proved that an indecomposable quasifinite weightW(Λ,n)(1)-module is a module of the intermediate series if Λ is not isomorphic to ℤ.
Supported by NSF grant no. 10471091 of China and two grants “Excellent Young Teacher Program” and “Trans-Century Training
Programme Foundation for the Talents” from the Ministry of Education of China. 相似文献
15.
V. K. Kharchenko 《Algebra and Logic》1997,36(2):133-144
Let L be a finite-dimensional restricted differential Lie C-algebra of R-continuous derivations of a prime ring R of characteristic
p>0, with generalized centroid C. We prove that if the associative inner part of L is quasi-Frobenius then R contains a nonzero
element a and elements v1,…,vn, such that for any x∈R we have the expansion
, where
are homorphisms of right RL-modules
. This gives rise to a certain relation on a ring over some subring, known as Shirshov local finiteness. The structure of
(R, RL)-subbimodules in a left Martindale ring of quotients is elucidated.
Supported by RFFR grant No. 95-01-01356a, and by the CONACYT of Mexico, Catedra Patrimonial 940411.
Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 219–238, March–April, 1997. 相似文献
16.
Ludvik Janos 《Annali di Matematica Pura ed Applicata》1977,112(1):273-283
Summary We consider the boundary value problem αz″(x)+m(x)y(x)=0, αy″(x)+p(x)z(x)=0, xε[0, 1], y(0)=y(1)=z(0)=0, where the functions m(x) and p(x) are assumed integrable and positive everywhere in [0, 1]. As the main result we obtain the inequalities
for n=1, 2, ... where δn(m, p) stands for the product
of the first n eigenvalues αi(m, p) of the above system and where δn(m) abbreviates δn(m, m).
Entrata in Redazione il 6 febbraio 1976. 相似文献
17.
J. S. Hwang 《数学学报(英文版)》1998,14(1):57-66
Letf(X) be an additive form defined by
wherea
i
≠0 is integer,i=1,2…,s. In 1979, Schmidt proved that if ∈>0 then there is a large constantC(k,∈) such that fors>C(k,∈) the equationf(X)=0 has a nontrivial, integer solution in σ1, σ2, …, σ3,x
1,x
2, …,x
3 satisfying
Schmidt did not estimate this constantC(k,∈) since it would be extremely large. In this paper, we prove the following result 相似文献
18.
Summary Let
a plane angle of opening α∈(π, 2π). LetP
D andP
N the Dirichlet and Neumann problems associated to the Poisson equation in
. ForP
D andP
N it is proved non existence of solution in L
p
(
) whenp=2/(1±π/α). In other words, the ranges of elliptic operators naturally associated toP
D andP
N are not-closed in L
p
(
) forp=2/(1±π/α).
Sunto Sia } un angolo piano di apertura α∈(π, 2π). SianoP D eP N i problemi di Dirichlet e di Neumann associati all'equazione di Poisson in . PerP D eP N si prova non esistenza di soluzioni in L p ( ) quandop=2/(1±π/α). Vale a dire i ranges degli operatori ellittici naturalmente associati aP D eP N sono non-chiusi in π--AgBrα K L p ( ) perp=2/(1±π/α).相似文献
19.
J. C. Gupta 《Proceedings Mathematical Sciences》2000,110(4):415-430
Let G
n,k
be the set of all partial completely monotone multisequences of ordern and degreek, i.e., multisequencesc
n(β1,β2,…, β
k
), β1,β2,…, βk
= 0,1,2,…, β1+β2 + … +β
k
≤n,c
n(0,0,…, 0) = 1 and
whenever β0 ≤n - (β1 + β2 + … + β
k
) where Δc
n(β1,β2,…, β
k
) =c
n(β1 + 1, β2,…, β
k
)+c
n(β1,β2+1,…, β
k
)+…+c
n (β1,β2,…, β
k
+1) -c
n(β1,β2,…, β
k
). Further, let Π
n,k
be the set of all symmetric probabilities on {0,1,2,…,k}
n
. We establish a one-to-one correspondence between the sets G
n,k
and Π
n,k
and use it to formulate and answer interesting questions about both. Assigning to G
n,k
the uniform probability measure, we show that, asn→∞, any fixed section {it{cn}(β1,β2,…, β
k
), 1 ≤ Σβ
i
≤m}, properly centered and normalized, is asymptotically multivariate normal. That is,
converges weakly to MVN[0, Σ
m
]; the centering constantsc
0(β1, β2,…, β
k
) and the asymptotic covariances depend on the moments of the Dirichlet (1, 1,…, 1; 1) distribution on the standard simplex
inR
k. 相似文献
20.
For a big number of varieties
of groups close to Engelian, it is proved that a variety of lattice-ordered groups generated by all linearly ordered groups
in the class
does not coincide with the variety
of all o-approximable lattice-ordered groups.
Supported by FP “Universities of Russia” grant No. UR.04.01.001.
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Translated from Algebra i Logika, Vol. 45, No. 1, pp. 20–27, January–February, 2006. 相似文献