Publication:
Double Operator Integration with applications to Quantised Calculus

dc.contributor.advisor Sukochev, Fedor en_US
dc.contributor.advisor Zanin, Dmitriy en_US
dc.contributor.author McDonald, Edward en_US
dc.date.accessioned 2022-03-23T11:45:44Z
dc.date.available 2022-03-23T11:45:44Z
dc.date.issued 2019 en_US
dc.description.abstract The theory of double operator integration provides a powerful set of tools for the study of spectral asymptotics of compact operators. We give a self-contained overview of the theory from its foundations, including a complete proof of the fundamental Peller's theorem. The theory is developed with the goal of proving a formula for the difference of complex powers of self-adjoint operators, which has recently been applied to problems in Connes' quantised calculus. The final two chapters give applications to the Conformal Trace Theorem for the Hausdorff measure of Julia sets of quadratic polynomials and to the characterisation of quantum differentiability on noncommutative Euclidean spaces. en_US
dc.identifier.uri http://hdl.handle.net/1959.4/64949
dc.language English
dc.language.iso EN en_US
dc.publisher UNSW, Sydney en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/3.0/au/ en_US
dc.subject.other Quantized calculus en_US
dc.subject.other Functional analysis en_US
dc.subject.other Harmonic analysis en_US
dc.title Double Operator Integration with applications to Quantised Calculus en_US
dc.type Thesis en_US
dcterms.accessRights open access
dcterms.rightsHolder McDonald, Edward
dspace.entity.type Publication en_US
unsw.accessRights.uri https://purl.org/coar/access_right/c_abf2
unsw.identifier.doi https://doi.org/10.26190/unsworks/21615
unsw.relation.faculty Science
unsw.relation.originalPublicationAffiliation McDonald, Edward, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Sukochev, Fedor, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Zanin, Dmitriy, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.school School of Mathematics & Statistics *
unsw.thesis.degreetype PhD Doctorate en_US
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