Nonlinear evolution systems and green's function

In this paper, we will introduce how to apply Green's function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen's principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green's function of the linearized system and micro-local analysis, such as frequency decomposition and so on.     

Shepard-Lagrange算子的逼近

本文建立了Shepard-Lagrange算子逼近的正逆定理,证明了可以利用高阶光滑模来刻画Shepard-Lagrange算子的逼近性质.从而说明了Shepard-Lagrange算子比一般的Shepard算子具有更好的逼近性质.进一步,所用光滑模的阶梯函数非常广泛,这是多项式逼近所不具有的.     

ON APPROXIMATION PROPERTIES OF NON-CONVOLUTION TYPE NONLINEAR INTEGRAL OPERATORS-Dedicated to Professor Paul L. Butzer on his 80th Birthday

In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t））dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as （x,λ） → （x0, λ0） in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]     

On the Riemann Summability of Fourier Integrals and Real Hardy Spaces

We consider the Riemann means of single and multiple Fourier integrals of functions belonging to L¹ or the real Hardy spaces defined on ℝⁿ, where n ≥ 1 is an integer. We prove that the maximal Riemann operator is bounded both from H¹(ℝ) into L¹(ℝ) and from L¹(ℝ) into weak –L¹(ℝ). We also prove that the double maximal Riemann operator is bounded from the hybrid Hardy spaces H^(1,0)(ℝIsup2), H^(0,1)(ℝ²⁾ into weak –L¹(ℝ²). Hence pointwise Riemann summability of Fourier integrals of functions in H^(1,0) ∪ H^(0,1)(ℝ²) follows almost everywhere.The maximal conjugate Riemann operators as well as the pointwise convergence of the conjugate Riemann means are also dealt with.     

关于Szabados的一个问题在L1尺度下的解答

Szabados在[6]中考虑了在(-1,1)中没有零点的n次仅有实零点的代数多项式的点态估计。本文将Szabados的问题加以一般化,在L~1尺度下考虑问题,并取得了相应的结果。     

关于正系数多项式导数的点态不等式

本文讨论正系数多项式导数的点态不等式,建立相应的结果。     

向量丛动力系统研究註记(Ⅱ)──部份1

过去,向量丛线性动力系统的整体线性性质研究已经显得相当广泛。现在,我们提议研究这种线性系统的扰动性质。我们要考虑的这种扰动系统将不再是线性的,但要研究的性质一般仍是整体性的。再者我们感兴趣的为非一致双曲性。在本文中我们给出了这种扰动的恰当的定义。它虽表现得有几分不太通常,然而它较深地植根于有关微分动力系统理论的典泛方程组中。这里一般的问题是要观察,当扰动发生后,原给系统的何种性质得以保持下来。本文的全部内容是要建立这种类型的一个定理。     

关于Erceg伪度量与点式伪度量的一点注记

文[13]曾证明Erceg伪度量与史福贵提出的点式伪度量等价.本文指出[13]中的定理1是错误的,进而指出Erceg伪度量与点式伪度量是不等价的.     

A space <Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>(<Emphasis Type="Italic">X</Emphasis>) is dominated by irrationals if and only if it is<Emphasis Type="Italic"> K</Emphasis>-analytic

Summary We prove that, for any Tychonoff X, the space C_p(X) is K-analytic if and only if it has a compact cover {K_p: p } such that K_p subset K_q whenever p,q and p q. Applying this result we show that if C_p(X) is K-analytic then C_p(X) is K-analytic as well. We also establish that a space C_p(X) is K-analytic and Baire if and only if X is countable and discrete.     

Continuity and Representation of Gaussian Mehler Semigroups

We present sufficient conditions on a Gaussian Mehler semigroup on a reflexive Banach space Eto be induced by a single positive symmetric operator Q \in , and give a counterexample which shows that this representation theorem is false in every nonreflexive Banach space with a Schauder basis. We also show that the transition semigroup of a Gaussian Mehler semigroup on a separable Banach space Eacts in a pointwise continuous way, uniformly on compact subsets of E, in the space BUC(E) of bounded uniformly continuous real-valued funtions on E. The transition semigroup is shown to be strongly continuous on BUC(E) if and only if S(t) = Ifor all t 0