%0 Journal Article
%T Bergman空间上的Toeplitz算子的乘积有限和问题<br>The Finite Sum Problem of the Product of Toeplitz Operators on Bergman Spaces
%A 关印
%A 王焕然
%A 崔姝宁
%J Pure Mathematics
%P 500-507
%@ 2160-7605
%D 2020
%I Hans Publishing
%R 10.12677/PM.2020.105061
%X <p align=\"justify\">
	本文讨论了Bergman空间上两个形如T<sub>fk</sub>，T<sub>gk</sub>的Toeplitz算子，其中假设g<sub>k</sub>=g<sub>1</sub><sup>(k)</sup>+g<sub>2</sub><sup>(k)</sup>，g<sub>1</sub><sup>(k)</sup>=<img alt=\"\" src=\"Edit_d0c3dade-8f2c-46cd-8dfc-fd47546aad6c.png\" />a<sub>j</sub><sup>(k)</sup> z<sup>j</sup>，g<sub>2</sub><sup>(k)</sup>=<img alt=\"\" src=\"Edit_b854aa91-368c-41c3-bca2-7f21c6fd7d98.png\" />b<sub>j</sub><sup>(k)</sup>z<sup>j</sup>∈H<sup>∞</sup>(D)；f<sub>k</sub>∈L<sup>∞</sup>(D,dA)。f<sub>k</sub>(re<sup>iθ</sup>)=<img alt=\"\" src=\"Edit_60384fcc-2eec-4ab1-a905-1b2a130f48bf.png\" />f<sub>p</sub><sup>(k)</sup>(r)e<sup>ipθ</sup>(1≤k≤N)。探究Toeplitz算子Tfk，Tgk的有限乘积有限和的相关问题，分析计算得到了其为零算子的一个必要条件。<br />
This paper discusses two Toeplitz operators as T<sub>fk</sub>, T<sub>gk</sub> in Bergman space. In case g<sub>k</sub>=g<sub>1</sub><sup>(k)</sup>+g<sub>2</sub><sup>(k)</sup>, g<sub>1</sub><sup>(k)</sup>=<img alt=\"\" src=\"Edit_00fad3b5-15fe-41a3-b283-7cd76a235076.png\" />a<sub>j</sub><sup>(k)</sup> z<sup>j</sup>, g<sub>2</sub><sup>(k)</sup>=<img alt=\"\" src=\"Edit_bfbafc2b-a947-41e1-9c26-c5a6d60ff637.png\" />b<sub>j</sub><sup>(k)</sup>z<sup>j</sup>∈H<sup>∞</sup>(D); f<sub>k</sub>∈L<sup>∞</sup>(D,dA). f<sub>k</sub>(re<sup>iθ</sup>)=<img alt=\"\" src=\"Edit_96d01ad0-1616-4350-9a6f-6687b4f504e5.png\" />f<sub>p</sub><sup>(k)</sup>(r)e<sup>ipθ</sup>(1≤k≤N). This paper explores the related problems of the sum of the finite products of the two Toeplitz operators as Tfk, Tgk under a large amount of data and calculations. A necessary condition of zero operator is obtained (N).
</p>
%K Bergman空间，Toeplitz算子，Mellin变换<br>Bergman Space
%K Toeplitz Operator
%K Mellin Transform
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=35609