一类再生Hilbert空间上偏微分算子的有界性(英文)

研究了一类再生Hilbert空间上偏微分算子的有界性,得到了偏微分算子有界的一个充分必要条件,推广了文献[1]中的结果.     

一类再生Hilbert空间上偏微分算子的有界性

研究了一类再生Hilbert空间上偏微分算子的有界性,得到了偏微分算子有界的一个充分必要条件,推广了文献中的结果．     

期权定价的小波方法

基于Daubechies正交小波,对微分算子进行小波近似,从而求解Black-Scholes方程,为期权定价提出了一种新的尝试.通过偏微分算子和小波系数的稀疏化,相对二叉树法,大大减少了计算量,提高了运算速度.     

Hilbert空间中的紧K-框架

K-框架是框架的一种推广.本文在Hilbert空间将紧框架推广到K-框架上,引入紧K-框架的概念.通过紧K-框架的算子K和合成算子给出紧K-框架的算子刻画,并利用紧K-框架的算子K给出紧K-框架成为紧框架的一个充要条件.还讨论紧K-框架的构造以及两个紧K-框架集的包含与涉及的算子K的相互关系.     

无穷矩阵拓扑代数的理想(Ⅰ)(英文)

本文给出了所有弱紧算子 ,强紧算子 ,Mackey紧算子 ,构成无穷矩阵拓扑下相同紧集的特征的刻画 .     

AM-紧算子的分解(英文)

给出了AM-紧算子,通过具有序连续范数的Banach lattice进行分解,且其中一个因子是AM-紧算子的结论.同时给出了正的AM-紧算子的一些结论.最后对于Dunford-Pettis算子考虑了同样的问题.     

一类非主型偏微分算子局部可解性的必要条件

<正> 一 自从H.Lewy提出了第一个不可解算子之后,偏微分算子的可解性问题受到许多人的注意.现在,对于这一课题的研究,已经取得了相当一般的结果. 一个具C~∞系数的线性偏微分算子P(x,D),我们说它在分布意义下是局部可解的,是指:在Ω中x_o∈Ω,存在x_o的一个邻域U,使得f∈C_o~∞(U),有P(x,D)u=f成立.     

Bergman空间A_α~p(B_n)上加权复合算子的紧差

该文研究了Bergman空间A_α~p(B_n)上加权复合算子差的紧性问题.给出了两个加权复合算子之差为紧算子的一些充分和必要判据.同时也给出了某个加权复合算子与有限个加权复合算子之和的差为紧算子的一个完全刻画.     

小加权α-Bloch空间上的复合算子

讨论了单位圆盘上小加权α-Bloch空间上复合算子的有界性和紧性,得到了复合算子是有界算子或紧算子的充分必要条件.     

不同Bers型空间之间的加权复合算子

该文讨论了单位圆盘上不同Bers型空间之间的加权复合算子的有界性、紧性和弱紧性, 给出了一些充分必要的判别条件, 特别地得到不同Bers型空间上加权复合算子的紧性与弱紧性的等价性. 这些推广了经典的复合算子与乘法算子的相关结论. 该文同时也给出了Bers型空间上复合算子的Fredholm性和闭值域问题的刻画, 完善了文献[6]中结论.     

CONSTRUCTION OF GEOMETRIC PARTIAL DIFFERENTIAL EQUATIONS FOR LEVEL SETS

Geometric partial differential equations of level-set form are usually constructed by a variational method using either Dirac delta function or co-area formula in the energy functional to be minimized. However, the equations derived by these two approaches are not consistent. In this paper, we present a third approach for constructing the level-set form equations. By representing various differential geometry quantities and differential geometry operators in terms of the implicit surface, we are able to reformulate three classes of parametric geometric partial differential equations （second-order, fourth-order and sixth- order） into the level-set forms. The reformulation of the equations is generic and simple, and the resulting equations are consistent with their parametric form counterparts. We further prove that the equations derived using co-area formula are also consistent with the parametric forms. However, these equations are of much complicated forms than these given by the equations we derived.     

SUFFICIENT CONDITIONS FOR LOCAL SOLVABILITY OF LEFT INVARIANT LPDOS ON THE GROUPS OF TYPE H

Some sufficient conditions are established for local solvability of inhomogeneous left invariant partial differential operators on the groups of type H. First some general sufficient conditions are derived for local solvablity of left invariant operators on the groups of type H. Then by asing these results the author discusses the local solvability of a special class of inhomogeneous left invariant operators on this type of groups.     

Noether, partial Noether operators and first integrals for a linear system

We obtain Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a system of two linear second-order ordinary differential equations (ODEs) with variable coefficients. The canonical form for a system of two second-order ordinary differential equations is invoked and a special case of this system is studied for both Noether and partial Noether operators. Then the first integrals with respect to Noether and partial Noether operators are obtained for the linear system under consideration. We show that the first integrals for both the Noether and partial Noether operators are the same. This can give rise to further studies on systems from a partial Lagrangian viewpoint as systems in general do not admit Lagrangians.     

Existence of the Møller wave operators in quantum scattering theory

Existence of the wave operators of quantum mechanical scattering theory is established. The Hamiltonians are constant coefficient partial differential operators and perturbations of them by variable coefficient linear partial differential operators. The coefficients may be short range in the usual sense but they may also be oscillating. The problem of establishing existence is reduced to that of approximating solutions of a certain partial differential equations on cones in phase space. The proof is based on a refinement of Cook's argument. Research supported in part by a fellowship, awarded by the University of Toledo.     

Inverse Problems on the Least Eigenvalue

Some uniqueness theorems on the least eigenvalue are provided for wide classes of self-adjoint operators: differential operators with operator-valued potentials, higher-order partial differential operators and the p-Laplacian.     

New proofs and generalisations of theorems of existence and uniqueness for the goursat problem

Abstract theorems of existence and uniqueness are proved for a differential equation whose solution takes its values in a sequence of Banach spaces called a Banach filtration (a notion introduced by F. Treves). The abstract theorems are then applied to obtain existence and uniqueness theorems of a classical nature bearing on that generalization of the Cauchy problem of partial differential equations known as the Goursat problem. All the results so obtained remain true in the case when the equations involve more general operators than partial differential operators (e.g., pseudo-differential operators)     

Separable anisotropic differential operators and applications

The nonlocal boundary value problems for anisotropic partial differential-operator equations with a dependent coefficients are studied. The principal parts of the appropriate generated differential operators are nonself-adjoint. Several conditions for the maximal regularity and the fredholmness in Banach-valued Lp-spaces of these problems are given. These results permit us to establish that the inverse of corresponding differential operators belongs to Schatten q-class. Some spectral properties of the operators are investigated. In applications, the nonlocal BVP's for quasielliptic partial differential equations and for systems of quasielliptic equations on cylindrical domain are studied.     

一类具重特征线性偏微分算子的局部可解性

运用Ｇａｒｄｉｎｇ不等式和Ｆｅｆｅｒｍａｎ－Ｐｈｏｎｇ不等式，建立了一类具实主会征的线性偏微分算子的局部可解性。