Show simple item record

dc.contributor.advisorPark, Efton
dc.contributor.authorHellerman, Nathanaelen_US
dc.date.accessioned2018-12-19T19:51:05Z
dc.date.available2018-12-19T19:51:05Z
dc.date.created2018en_US
dc.date.issued2018en_US
dc.identifieraleph-005160262en_US
dc.identifier.urihttps://repository.tcu.edu/handle/116099117/22833
dc.description.abstractLet C(S^1) x Zn be the crossed product algebra, where the group Zn enacts a rotation on the complex coordinate z. We consider the algebra of Toeplitz operators with symbols from the crossed product algebra C(S^1) x Zn. We find the K-theory of this Toeplitz algebra and a formula to calculate the Fredholm index of an operator from it. Similarly, we consider the crossed product algebra of C(S^3) x Zn, where the group Zn enacts a rotation on one of the complex coordinates of S^3. We consider the algebra of Toeplitz operators with symbols from the crossed product algebra C(S^3) x Zn. We find the K-theory of this Toeplitz algebra and a formula to calculate the Fredholm index of an operator from it. The index formula is the sum of n integrals which can be used to determine when two operators are in different homotopy classes, even if they have the same index.
dc.format.extent1 online resource (iii, 81 pages).en_US
dc.format.mediumFormat: Onlineen_US
dc.language.isoengen_US
dc.relation.ispartofTexas Christian University dissertationen_US
dc.relation.ispartofUMI thesis.en_US
dc.relation.ispartofTexas Christian University dissertation.en_US
dc.subject.lcshToeplitz operators.en_US
dc.subject.lcshAlgebra.en_US
dc.titleToeplitz operators with symbols from certain rotation algebras and their index formulasen_US
dc.typeTexten_US
etd.degree.departmentDepartment of Mathematics
etd.degree.levelDoctoral
local.collegeCollege of Science and Engineering
local.departmentMathematics
local.academicunitDepartment of Mathematics
dc.type.genreDissertation
local.subjectareaMathematics
etd.degree.nameDoctor of Philosophy
etd.degree.grantorTexas Christian University


Files in this item

Thumbnail
This item appears in the following Collection(s)

Show simple item record