【摘要】：本文主要討論了線性算子動力系統(tǒng),并給出了若干結果.其研究內容主要涉及四個方面:其一,我們研究了在實或復的標量域上可分Hilbert空間上子空間圓盤循環(huán)算子,給出了圓盤循環(huán)算子投影,核等重要性質.此外,我們舉出一個例子說明了M-圓盤循環(huán)不一定能推出M-圓盤傳遞.我們還給出了子空間-supercyclic半群的性質以及判定子空間-supercyclic半群的兩個標準.其二,介紹了如何去判定一個算子是super凸循環(huán)的.尤其給出了 Super凸循環(huán)標準.另外,我們也研究了(可逆的)雙邊加權位移算子的凸循環(huán)和super凸循環(huán)性質.其三,我們介紹了一個新的定義不交圓盤循環(huán).更具體地,我們給出不交圓盤blow-up/collapse性質和不交圓盤循環(huán)標準.此外,我們還研究了雙邊以及單邊加權位移算子的不交圓盤循環(huán)性質.最后,我們研究了從全純函數(shù)映射到Taylor展式的部分和的不交supercyclic算子.特別地,我們證明出Taylor-type算子組的不交超循環(huán)性質等價于不交su-percyclicity. 另外,我們給出一個判定 Taylor-type 算子組的不交 supercyclic 性質的充分條件.
[Abstract]:In this paper, the linear operator dynamical system is discussed, and some results are given. The main contents of this paper are as follows: first, we study the subspace circular disk operators on the scalar domain of real or complex Hilbert, and give some important properties such as the projection and kernel of the circular disk operators. In addition, we give an example to show that the M-disk cycle does not necessarily produce the M-disk transfer. We also give the properties of subspace--supercyclic Semigroups and two criteria for judging subspace--supercyclic Semigroups. Secondly, how to determine that an operator is a super convex loop is introduced. In particular, the Super convex cycle standard is given. In addition, we also study the convex cycle and super convexity of the (reversible) bilateral weighted displacement operator. Thirdly, we introduce a new definition of disjoint disk cycle. More specifically, we give the blow-up/collapse property of disjoint disk and the circular standard of disjoint disk. In addition, we also study the disjoint circular properties of bilateral and unilateral weighted displacement operators. Finally, we study the disjoint supercyclic operators of partial sum mapping from Holomorphic functions to Taylor expansions. In particular, we prove that the disjoint hypercyclic property of Taylor-type operator system is equivalent to disjoint su-percyclicity.. In addition, we give a sufficient condition to judge the disjoint supercyclic property of Taylor-type operator system.
【學位授予單位】：天津大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O177

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