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Lifting theorems for tuples of 3-iso...

Russo, Benjamin Peter.

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Lifting theorems for tuples of 3-isometric and 3-symmetric operators with applications.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lifting theorems for tuples of 3-isometric and 3-symmetric operators with applications./
作者:	Russo, Benjamin Peter.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	110 p.
附註:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10299053
ISBN:	9781369420760

Lifting theorems for tuples of 3-isometric and 3-symmetric operators with applications.
Russo, Benjamin Peter.

Lifting theorems for tuples of 3-isometric and 3-symmetric operators with applications. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 110 p.

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)--University of Florida, 2016.

An operator T is called a 3-isometry if there exists a B1(T*,T) and B 2(T*,T) such that (n/a) for all natural numbers n. A related class of operators, called 3-symmetric operators, have a similar definition. These operators have a connections with Sturm-Liouville theory and are natural generalizations of isometries and self-adjoint operators. We call an operator J a Jordan operator of order 2 if J = A + N, where A is either unitary or self-adjoint, N is nilpotent order 2, and A and N commute. As shown in the work of Agler, Ball and Helton, and joint work with McCullough, 3-symmetric and 3-isometric operators can be modeled as Sub-Jordan operators. We develop the extension of these theorems to the multi-variable case in relation to a conjecture of Ball and Helton. More specifically, we cover connections between the lifting theorems via spectral theory and the necessity of an extra condition unique to the multi-variable case. We also develop applications of both the one variable and multi-variable lifting theorem to disconjugacy for Sturm-Liouville operators and Schrodinger operators.

ISBN: 9781369420760Subjects--Topical Terms:

515831
Mathematics.

Lifting theorems for tuples of 3-isometric and 3-symmetric operators with applications.
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