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

紀錄類型:	書目-語言資料,手稿 : 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.
面頁冊數:	1 online resource (110 pages)
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:	click for full text (PQDT)
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. - 1 online resource (110 pages)

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

Thesis (Ph.D.)

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369420760Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Lifting theorems for tuples of 3-isometric and 3-symmetric operators with applications.
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245 1 0 $a Lifting theorems for tuples of 3-isometric and 3-symmetric operators with applications.
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300 $a 1 online resource (110 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
502 $a Thesis (Ph.D.) $c University of Florida $d 2016.
504 $a Includes bibliographical references
520 $a 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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
655 7 $a Electronic books. $2 local $3 554714
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690 $a 0642
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710 2 $a University of Florida. $b Mathematics. $3 1180793
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