R×R上到R的某类1-1映射的不存在性

In p.32 of [1] the following problem is posed: A problem on Peano mapping Let R be the set of positive rational integers with usual operation a+b≡s(a,b) and a·b≡m(a,b). Every one-to-one(Peano) mapping c=p(a,b) on R×R to all R may serve so associate with s(a,b) and m(a,b) two functions σand μ on R to R by the definitions σ(c)=σ(p(a,b))= s(a,b), and μ(c)=μ(p(a,b))= m(a,b). Does there exist a Peano mapping p(a,b) such that "addition commutes with multiplication" in the sense that σ(μ(c))=μ(σ(c))for all c of R? To illustrate, we note     

BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATION ON HERZ-TYPE SPACES

1 IntroductionLgt b E BMO(Rn) and 11 be a fractional integration with 0 < I < n. The commutator[b, II] generated by b and 11 is defined by[b, II]f(x) = b(x)llf(x) ~ II(sf)(x).S.Chanillolz] stated that the operator [b, II] is a bounded operator from LPI (R") on LPZ(R")for 1/Pz = 1/pl -- l/n and 1 < pl < n/l. Recently, Lu Shanzhen and Yang Dachun[9] studiedthe commutator [b,ll] on Herz spaces and a new class of Herz-type Hardy spaces introducedby them and established the correspondi…     

非对称Cantor集的Hausdorff中心测度

§ 1　 IntroductionThe class of Cantor sets is a typical one of sets in fractal geometry.Mathematicianshave paid their attentions to such sets for a long time.Itis well known that the Hausdorffmeasure of the Cantor middle- third set is1(see[1]) .Recently,Feng[3] obtained the exactvalues of the packing measure for a class of linear Cantor sets.Using Feng s method,Zhuand Zhou[5] obtained the exactvalue of Hausdorff centred measure of the symmetry Cantorsets.In this papar,we consider the Ha…     

Characterizations and Extensions of Lipschitz-α Operators

In this work, we prove that a map F from a compact metric space K into a Banach space X over F is a Lipschitz-α operator if and only if for each σ in X^＊ the map σoF is a Lipschitz-α function on K. In the case that K = [a, b], we show that a map f from [a, b] into X is a Lipschitz-1 operator if and only if it is absolutely continuous and the map σ→ （σ o f）＇ is a bounded linear operator from X^＊ into L^∞（[a, b]）. When K is a compact subset of a finite interval （a, b） and 0 〈 α ≤ 1, we show that every Lipschitz-α operator f from K into X can be extended as a Lipschitz-α operator F from [a, b] into X with Lα（f） ≤ Lα（F） ≤ 3^1-α Lα（f）. A similar extension theorem for a little Lipschitz-α operator is also obtained.     

E^3中零亏格闭曲面的几个整体定理

A Svec^[1] obtained some results on surfaces in E^3 by the method of quasi-analytic function.This paper gives several global properties on closed surfaces with qenus zero by the similar method, obtains the main result that a closed special Weingartan surface with qeus zero in E^3 is a sphere,gives wo conditions for two surfaces with congrence property,and proves that there is not closed Bonnet surface with qenus zero.     

The best quadrature based on given Hermite information for the Sobolev class KW~r[a,b]

As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. in [a, b]. For a function f∈KWr[a, b], its values and derivatives up to r -1 order at a set of nodes x are known. These values are said to be the given Hermite information. This work reports the results on the best quadrature based on the given Hermite information for the class KWr[a. b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product, the best interpolation formula for the class KWr[a, b] is also obtained.     

Degree Conditions for k-Hamiltonian [a,b]-factors

Let a,b,k be nonnegative integers with 2≤a相似文献   

完全测度空间上的 Fubini 定理

<正> 对于定义在矩形I={(x,y),a≤x≤b,c≤y≤d}上的连续函数f(x,y),我们有古典的公式:integral from I f(x,y)dxdy=ingetral from a to b[ingetral from c to d f(x,y)dy]dx=integral from a to b f(x,y)dx]dy。本文推广累次积分公式,给出完全测度空间上的Fubini 定理。给定两个测度空间(X,(?),μ),(y,(?),v),称X×Y 中集A×B 为矩形,若A∈(?),B∈(?),     

NEAR CIRCULARITY AND ZEROS OF THE ERROR FUNCTION FOR CHEBYSHEV APPROXIMATION 0N A DISK

1. Introduction A classical characterization of the best Chebyshev polynomialapproximation to a real continuous function on an interval [a, b]is the equioscillation property of the optimal error function.Consequently, when approximating f∈C [a, b] by polynomials of     

Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space

It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in C[a,b] or L2[a,b].In this paper,the representation of the...     

Lp-gradient estimates for the commutators of the Kato square roots of second-order elliptic operators on ℝn

Let L=-div(A▽) be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln(Rn)(n> 2),is bounded from the homogenous Sobolev space L1p(Rn) to Lp(Rn)(p-(L)     

ON J-SELFADJOINT EXTENSION OF THE PRODUCT OF TWO nTH-ORDER J-SYMMETRIC ORDINARY DIFFERENTIAL OPERATORS ON [a,b]

The problem of J-selfadjointness of the product of two nth-order J-symmetric operators on [a,b] is studied. We give a condition to ensure that the product operator is a J-selfadjoint extension.     

Strong 3-commutativity preserving maps on standard operator algebras

Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B(X). A map Φ :A →A is said to be strong 3-commutativity preserving if [Φ(A), Φ(B)]3 = [A,B]3 for all A,B∈ A, where[A,B]3 is the 3-commutator of A,B defined by[A, B]3 = [[[A, B],B],B] with [A,B] = AB-BA. The main result in this paper is shown that.,if Φ is a surjective map on A, then Φ is strong 3-commutativity preserving if and only if there exist a functional h : A →F and a scalar λ∈ F with λ~4 = 1 such that Φ(A)=λ A+h(A)I for all A ∈ A.     

Lie Triple Derivations on von Neumann Algebras

Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A.     

A Necessary and Sufficient Condition on Convergence of Bounded Linear Operators in the Space of Continuous Functions

Korovkin[1]gave a necessary and sufficient condition on lineax positiveapproximation in C[a,b].In this note,we give such a condition on general boundedapproximation in C[a,b]     

有限不变测度与一维扩散过程

<正> 本文沿用[2]或[3]中的记号. 对于微分算符Ω: Ωu=(a(x)u′)′+b(x)u′+c(x)u(1) a(x)>0,c(x)≤0,a(x),b(x)连续可微,c(x)连续以及它的形式共轭算符Ω: Ωv=(a(x)v′)′-(b(x)v)′+c(x)v(2)我们将说明:在c(x)0时Ω导出的满足局部边值条件的马氏过程P(t,x,Γ)(确切含义见[2]或[3]中定义4.5.1,4.5.4及4.5.5)不存在有限不变测度;在c(x)≡0时Ω导出的满足局部边值条件的马氏过程P(t,x,Γ)如果存在有限不变测度,则必是绝对连续的且其密度满足共轭方程.     

具有粗糙核的多线性算子在Herz型空间的有界性

§ 1　Introduction and main resultsLet b∈BMO(Rn) and T be a standard Calderon-Zygmund singular integral operator.Define the commutator[b,T] as follows.[b,T] f(x) =b(x) Tf(x) -T(bf) (x) .In [3 ] ,the boundedness ofthe commutator[b,T] wasestablished on Lp(Rn) .There are thesimilar results in [1 ,2 ] when the commutator was substituted with the multilinearoperators generated by the singular integral operator T and a Taylor series A(see thedefinition below) .Recently,many mathematicians h…     

Commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of Homogeneous type of finite measure

Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on Lp (X), 1 ＜ p ＜∞. We give a sufficient condition on the kernel k(x,y) of Tso that when a function b ∈ BMO (X) ,the commutator [b, T] (f) = T (b f) - bT (f) is aounded on spaces Lp for all p, 1 ＜ p ＜∞.     

Equidistribution of Expanding Translates of Curves in Homogeneous Spaces with the Action of(SO(n,1))k

Let X = G/Γ be a homogeneous space with ambient group G containing the group H =(SO(n, 1))^k and x ∈ X be such that Hx is dense in X. Given an analytic curve ? : I = [a, b] → H,we will show that if φ satisfies certain geometric condition, then for a typical diagonal subgroup A ={a(t) : t ∈ R} ? H the translates {a(t)?(I)x : t > 0} of the curve ?(I)x will tend to be equidistributed in X as t → +∞. The proof is based on Ratner’s theorem and linearization technique.     

Commutators with finite spectrum II

The purpose of this paper is to study derivations d, d′ defined on a Banach algebra A such that the spectrum a（[dx, d′x]） is finite for all x ∈ A. In particular we show that if the algebra is semisimple, then there exists an element a in the socle of A such that [d, d′] is the inner derivation implemented bv a.