Sz(a)sz-Kantorovich算子的保形性质

本文讨论了Szasz-Kantorovich算子的保形问题，得到了算子在保持函数曲线几何性质方面的一系列结果，结果表明该算子在保形方面与Szasz-Mirakjan算子是有差异的。     

齐型空间上的Poisson算子与广义Carleson测度

该文在齐型空间上定义了一类广义Carleson测度和Poisson型位势算子，该算子具有与Poisson核相似的性质，研究了该算子在Lp、Hp和Tent空间与Lorentz空间上的有界性.     

一类可靠性模型时间依赖解的渐近性质

研究了带无穷多个部件的，由一个可靠机器，一个不可靠机器与一个缓冲库构成的系统解的渐近性质．先讨论了对应于该系统的主算子的谱特征并且得到了在虚轴上除了0点外其它所有点都属于该主算子的豫解集，0是该主算子及其共轭算子几何重数为1的特征值．然后将该结果与作者以前的结果结合起来推出该系统的时间依赖解当时刻趋向于无穷时趋向于该系统的稳态解．     

二元Baskakov算子的逼近

在［１］中构造了一系列一元及多元线性算子，其中包括二元Ｂａｓｋａｋｏｖ算子，本文讨论该算子在Ｃ空间的逼近性质．     

多元Meyer－KonigandZeler算子的一致逼近

本文构造一种二元Ｍｅｙｅｒ－ＫｏｎｉｇａｎｄＺｅｌｅｒ算子，讨论该算子在正方形域上的一致逼近，建立了两种形式的等价定理     

M/Mk,B/1算子的豫解集

首先运用Phillips定理和Fattorini定理证明M／M^k，^B／1排队模型概率瞬态解的存在唯一性，然后通过研究对应于M／M^k，^B／1排队模型的主算子的共轭算子的豫解集得到该主算子的豫解集：在虚轴上除了零点外其它所有点都属于该主算子的豫解集．     

二维Szasz－Durrmeyer算子在C空间的逼近定理

本文在上定义了一个二维的Ｓｚａｓｚ－Ｄｕｒｒｍｅｙｅｒ算子，并给出了该算子在Ｃ空间上的逼近等价定理．     

Feller-Trotter概率型算子对有界变差函数的收敛速度

本文运用概率方法研究了Feller-Trotter概率型算子对有界变差函数的收敛速度。由于该算子包括许多常见的算子,从而由关于该算子的一般结论可导出许多常见算子对有界变差。函数的收敛速度。作为一般结论的应用,本文列举了Baskakov算子、Szasz-Mirakjan算子、Gauss-Weierstrass算子、Gramma算子、Post-Gamma算子对有界变差函数的收敛速度。其中,关于Szasz-Mirakjan算子的结论推广并改进了Fuhua Cheng的结论,其它结论是作者首次得到。     

一维常系数双曲型方程每步过滤解法的稳定性与误差分析

考虑一维常系数双曲型方程的高阶数值解法，引进了一种稳定性过滤算子FN，最后从理论和数值实验上分析了该过滤算子对数值解稳定性和精度的影响．     

无界区域R1上的吊桥方程的全局吸引子

本文研究了无界区域R^1上的吊桥方程，运用算子分解和带权空间上构造紧算子的方法，得到了该方程在无界区域R^1上存在全局吸引子．     

Nilpotent operators similar to irreducible operators

We give a necessary and sufficient condition for the nilpotent operators to be similiar to irreducible operators, and give an answer to D. A. Herrero Conjectures for nilpotent operators.     

Essentially subnormal operators

An operator is essentially subnormal if its image in the Calkin algebra is subnormal. We shall characterize the essentially subnormal operators as those operators with an essentially normal extension. In fact, it is shown that an essentially subnormal operator has an extension of the form ``normal plus compact'.

The essential normal spectrum is defined and is used to characterize the essential isometries. It is shown that every essentially subnormal operator may be decomposed as the direct sum of a subnormal operator and some irreducible essentially subnormal operators. An essential version of Putnam's Inequality is proven for these operators. Also, it is shown that essential normality is a similarity invariant within the class of essentially subnormal operators. The class of essentially hyponormal operators is also briefly discussed and several examples of essentially subnormal operators are given.

     

Super-Ergodic operators

The aim of this work is to study operators naturally connected to Ergodic operators in infinite-dimensional Banach spaces, such as Uniform-Ergodic, Cesaro-bounded and Power-bounded operators, as well as stable and superstable operators. In particular, super-Ergodic operators are introduced and shown to be strictly between Ergodic and Uniform-Ergodic operators, and that any power bounded operator is super-Ergodic in a superreflexive space. New relationships between these operators are shown, others are proven to be optimal or can be ameliorated according to structural properties of the Banach space, such as the superreflexivity or with unconditional basis.

     

Products of integral-type operators and composition operators between Bloch-type spaces

A complete picture on the boundedness and compactness of the products of integral-type operators and composition operators between Bloch-type spaces of holomorphic functions on the unit disk is given in this paper.     

Triebel-lizorkin space estimates for multilinear operators of sublinear operators

In this paper, we obtain the continuity for some multilinear operators related to certain non-convolution operators on the Triebel-Lizorkin space. The operators include Littlewood-Paley operator and Marcinkiewicz operator.     

Positive set‐operators of low complexity

The powerset operator, ??, is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them ?‐operators. The question we address in this paper is: How is the class of ?‐operators generated ? It is shown that every positive ?‐operator Γ such that Γ(??) ≠ ??, is finitely generated from ??, the identity operator Id, constant operators and certain trivial ones by composition, ∪ and ∩. This extends results of [3] concerning bounded positive operators.     

Quasidifferentials and maximal normal operators

Quasidifferentials are studied with the theory of maximal normal operators. The quasidifferential of a normally quasidifferentiable function is a pair of upper and lower semicontinuous operators, which are special maximal normal operators. The function sum of the upper and lower semicontinuous operators is the Clarke subdifferential of this function. Basic calculus and minimal forms of quasidifferentials are also discussed.     

Unitary equivalence of one-parameter groups of Toeplitz and composition operators

The composition operators on H² whose symbols are hyperbolic automorphisms of the unit disk fixing ±1 comprise a one-parameter group and the analytic Toeplitz operators coming from covering maps of annuli centered at the origin whose radii are reciprocals also form a one-parameter group. Using the eigenvectors of the composition operators and of the adjoints of the Toeplitz operators, a direct unitary equivalence is found between the restrictions to zH² of the group of Toeplitz operators and the group of adjoints of these composition operators. On the other hand, it is shown that there is not a unitary equivalence of the groups of Toeplitz operators and the adjoints of the composition operators on the whole of H², but there is a similarity between them.     

On the closability of paranormal operators

We show two examples of operators acting on some Hilbert space and having invariant domains: a paranormal operator, which is not closable and a paranormal and closable operator, which closure is not paranormal. We start by establishing some general lemmas and propositions associating the families of operators mentioned above.