共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, the boundedness of Toeplitz operator T
b(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ε
(ℝn) is discussed from L
p(ℝn) to L
q(ℝn),
, and from L
p(ℝn) to Triebel-Lizorkin space
. We also obtain the boundedness of generalized Toeplitz operator Θ
α0
b
from L
p(ℝn) to L
q(ℝn),
. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator
T
b(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L
p(ℝn), 1 < p < ∞. 相似文献
2.
DENG Yanjuan & WANG Changping LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2006,49(1):75-85
Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian structure with the conformal transformation group O(3,2)/{±1}. In this paper, we study local conformal invariants of time-like surfaces in Q3 and dual theorem for Willmore surfaces in Q3. Let M (?) R13 be a time-like surface. Let n be the unit normal and H the mean curvature of the surface M. For any p ∈ M we define S12(p) = {X ∈ R13 (X - c(P),X - c(p)) = 1/H(p)2} with c(p) = P 1/H(p)n(P) ∈ R13. Then S12 (p) is a one-sheet-hyperboloid in R3, which has the same tangent plane and mean curvature as M at the point p. We show that the family {S12(p),p ∈ M} of hyperboloid in R13 defines in general two different enveloping surfaces, one is M itself, another is denoted by M (may be degenerate), and called the associated surface of M. We show that (i) if M is a time-like Willmore surface in Q3 with non-degenerate associated surface M, then M is also a time-like Willmore surface in Q3 satisfying M = M; (ii) if M is a single point, then M is conformally equivalent to a minimal surface in R13. 相似文献
3.
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
4.
Furstenberg family and chaos 总被引:3,自引:0,他引:3
Jin-cheng XlONG~ Jie L Feng TAN School of Mathematical Sciences South China Normal University Guangzhou China 《中国科学A辑(英文版)》2007,50(9):1325-1333
A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A■B and A∈F imply B∈F.For a given system (i.e.,a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family F, the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family F.In the present paper we explore the basic properties of the set of F-scrambled pairs of a system.The generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed. 相似文献
5.
Y. Nishimura 《Proceedings of the Steklov Institute of Mathematics》2006,252(1):212-224
For a simple complete multipolytope
in ℝn, Hattori and Masuda defined a locally constant function
on ℝn minus the union of hyperplanes associated with
, which agrees with the density function of an equivariant complex line bundle over a Duistermaat-Heckman measure when
arises from a moment map of a torus manifold. We improve the definition of
and construct a convex chain
on ℝn. The well-definiteness of this convex chain is equivalent to the semicompleteness of the multipolytope
. Generalizations of the Pukhlikov-Khovanskii formula and an Ehrhart polynomial for a simple lattice multipolytope are given
as corollaries. The constructed correspondence ⨑ub;simple semicomplete multipolytopes⫂ub; →; ⨑ub;convex chains⫂ub; is surjective
but not injective. We will study its “kernel.” 相似文献
6.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively. 相似文献
7.
N. I. Osetinskii 《Computational Mathematics and Modeling》2008,19(1):45-56
We consider the classification of generalized linear controllable systems over the field
= ℂ or
= ℝ under transformations defined by the action of the group GL
n
(
) × GL
n
(
). We review the recent results of Cobb, Helmke, Shayman, Zhou, Hinrichsen, O’Halloran, and others on the geometric structure
of the set of orbits C
n,m
(
) of generalized linear controllable systems, which in particular prove smoothness, compactness, and projectivity of C
n,m
(
) and evaluate its dimension. We show that C
n,m
(
) is a natural compactification of the set of orbits of ordinary linear controllable systems ∑
n,m
(
) and the boundary C
n,m
(
) − ∑
n,m
(
) consists of the orbits of singular generalized systems.
__________
Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 153–166, 2004. 相似文献
8.
We investigate the correlation between the constants K(ℝn) and
, where
is the exact constant in a Kolmogorov-type inequality, ℝ is the real straight line,
, L
l
p, p
(G
n) is the set of functions ƒ ∈ L
p
(G
n
) such that the partial derivative
belongs to L
p
(G
n
),
, 1 ≤ p ≤ ∞, l ∈ ℕn, α ∈ ℕ
0
n
= (ℕ ∪ 〈0〉)n, D
α
f is the mixed derivative of a function ƒ, 0 < μi < 1,
, and ∑
i=0
n
. If G
n
= ℝ, then μ0=1−∑
i=0
n
(α
i
/l
i
), μi = αi/l
i
,
if
, then μ0=1−∑
i=0
n
(α
i
/l
i
) − ∑
i=0
n
(λ/l
i
), μi = αi/ l
i
+ λ/l
i
,
, λ ≥ 0. We prove that, for λ = 0, the equality
is true.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 597–606, May, 2006. 相似文献
9.
The asymptotic expansions are studied for the vorticity
to 2D incompressible Euler equations with-initial vorticity
, where ϕ0(x) satisfies |d ϕ0(x)|≠0 on the support of
and
is sufficiently smooth and with compact support in ℝ2 (resp. ℝ2×T) The limit,v(t,x), of the corresponding velocity fields {v
ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω0(x). Moreover,
(ℤ2)) for all 1≽p∞, where
and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively. 相似文献
10.
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.
__________
Translated from Algebra i Logika, Vol. 44, No. 5, pp. 622–630, September–October, 2005. 相似文献
11.
In this paper, we study a class of Finsler metrics in the form
, where
is a Riemannian metric, β = b
i
y
i
is a 1-form, and ε and k ≠ 0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively
flat Finsler metrics with the constant flag curvature must be locally Minkowskian. 相似文献
12.
V. V. Makeev 《Journal of Mathematical Sciences》2005,131(1):5395-5400
Let ABCDE be a pentagon inscribed in a circle. It is proved that if
is a C4-generic smooth convex planar oval with four vertices (stationary points of curvature), then there are two similarities φ
such that the quadrangle φ(ABCD) is inscribed in
and the point φ(E)lies inside
, as well as two similarities ψ such that the quadrangle ψ(ABCD) is inscribed in
and ψ(E)lies outside
. Itisalsoprovedthatif n is odd, then any smoothly embedded circle γ ↪ ℝn contains the vertices of an equilateral (n + 1)-link polygonal line lying in a hyperplane of ℝn. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 241–251. 相似文献
13.
Yanping Chen Bolin Ma 《分析论及其应用》2007,23(2):112-128
Let (→b)=(b1,…,bm),bi∈Λβi(Rn),1≤i≤m,0<βi<β,0<β<1,[(→b),T]f(x)=∫Rn,(b1(x)-b1(y))…(bm(x)-bm(y)))K(x-y)f(y)dy where K is a Calder(o)n-Zygmund kernel.In this paper,we show that[(→b),T] is bounded from Lp (Rn) to Fβ,∞p(Rn),as well as[(→b,Iα)] from Lp(Rn) to Fβ,∞p(Rn),where 1/q=1/p-α/n. 相似文献
14.
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.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 379–389, July–August, 2006. 相似文献
15.
V. F. Molchanov 《Journal of Mathematical Sciences》2007,141(4):1432-1451
The two-sheeted hyperboloid
in ℝn can be identified with the unit sphere Ω in ℝn with the equator removed. Canonical representations of the group G = SO
0(n − 1, 1) on
are defined as the restrictions to G of the representations of the overgroup
= SO
0(n, 1) associated with a cone. They act on functions and distributions on the sphere Ω. We decompose these canonical representations
into irreducible constituents and decompose the Berezin form. Bibliography: 12 titles.
To the memory of my teacher F. A. Berezin
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 91–124. 相似文献
16.
WU Hao & LI Weigu School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,48(12):1670-1682
In this paper, we consider the following autonomous system of differential equations: x = Ax f(x,θ), θ = ω, where θ∈Rm, ω = (ω1,…,ωm) ∈ Rm, x ∈ Rn, A ∈ Rn×n is a constant matrix and is hyperbolic, f is a C∞ function in both variables and 2π-periodic in each component of the vector e which satisfies f = O(||x||2) as x → 0. We study the normal form of this system and prove that under some proper conditions this system can be transformed to an autonomous system: x = Ax g(x), θ = ω. Additionally, the proof of this paper naturally implies the extension of Chen's theory in the quasi-periodic case. 相似文献
17.
Isotropic bodies and Bourgain''''s problem 总被引:1,自引:0,他引:1
HE Binwu & LENG Gangsong Department of Mathematics Shanghai University Shanghai China 《中国科学A辑(英文版)》2005,48(5):666-679
Let K (?) Rn be a convex body of volume 1 whose barycenter is at the origin, LK be the isotropic constant of K. Finding the least upper bound of LK , being called Bourgain's problem, is a well known open problem in the local theory of Banach space. The best estimate known today is LK < cn1/4 log n, recently shown by Bourgain, for an arbitrary convex body in any finite dimension. Utilizing the method of spherical section function, it is proven that if K is a convex body with volume 1 and r1Bn2 (?) K (?) r2Bn2,(r1≥1/2, r2≤(?)/2), then (?) ≤(?) and find the conditions with equality. Further, the geometric characteristic of isotropic bodies is shown. 相似文献
18.
Let X = {X(t),t <σ} (σ is lifespan) be a birth and death process with explosion whose characteristic triple (Mα,MC,MD) of MX in terms of (α, C, D) and M. This means that a lot of given birth and death processes can be embedded in one and the same birth and death process. If κ∈ E and M = {κ},we decompose X into κX, κ∈ E. 相似文献
19.
We consider the moduli space
r
of polygons with fixed side lengths in five-dimensional Euclidean space. We analyze the local structure of its singularities
and exhibit a real-analytic equivalence between
r
and a weighted quotient of n-fold products of the quaternionic projective line
1 by the diagonal PSL(2,
)-action. We explore the relation between
r
and the fixed point set of an anti-symplectic involution on a GIT quotient Grℂ(2, 4)
n
/SL(4, ℂ). We generalize the Gel'fand—MacPherson correspondence to more general complex Grassmannians and to the quaternionic
context, and realize our space
r
as a quotient of a subspace in the quaternionic Grassmannian Grℍ(2, n) by the action of the group Sp(1)
n
. We also give analogues of the Gel'fand—Tsetlin coordinates on the space of quaternionic Hermitean marices and briefly describe
generalized action—angle coordinates on
r
. 相似文献
20.
Ai-hua FAN~ 《中国科学A辑(英文版)》2007,50(11):1521-1528
Let (∈n)≥0 be the Markov chain of two states with respect to the probability measure of the maximal entropy on the subshift space ∑A defined by Fibonacci incident matrix A.We consider the measure μλ of the probability distribution of the random series ∑∞n=0 εnλn (0 <λ< 1).It is proved that μλ is singular if λ∈ (0,√5-1/2) and that μλ is absolutely continuous for almost all λ∈ (√5-1/2,0.739). 相似文献