Title:
Modulation spaces, BMO and the Zak transform, and minimizing IPH functions over the unit simplex

dc.contributor.advisor Heil, Christopher E.
dc.contributor.author Tinaztepe, Ramazan en_US
dc.contributor.committeeMember Dieci, Luca
dc.contributor.committeeMember Lubinsky, Doron
dc.contributor.committeeMember Monteiro, Renato DC
dc.contributor.committeeMember Zhou, Hao Min
dc.contributor.department Mathematics en_US
dc.date.accessioned 2010-09-15T18:27:04Z
dc.date.available 2010-09-15T18:27:04Z
dc.date.issued 2010-07-07 en_US
dc.description.abstract This thesis consists of two parts. In the first chapter, we give some results on modulation spaces. First the relationship between the classical spaces and the modulation spaces is established. It is proved that certain modulation spaces defined on R² lie in the BMO space. Another result is that the Zak transform, a discrete time-frequency transform, maps a modulation space into a higher dimensional modulation space. And by using these results, an uncertainty principle for Gabor frames via modulation spaces is obtained. In the second part, we deal with optimization of an increasing positively homogeneous functions on the unit simplex. The class of increasing positively homogeneous functions is one of the function classes obtained via min-type functions in the context of abstract convexity. The cutting angle method is used for the minimization of this type functions. The most important step of this method is the minimization of a function which is the maximum of a number of min-type functions on the unit simplex. We propose a numerical algorithm for the minimization of such functions on the unit simplex and we mathematically prove that this algorithm finds the exact solution of the minimization problem. Some experiments have been carried out and the results of the experiments have been presented. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/34659
dc.publisher Georgia Institute of Technology en_US
dc.subject Cutting angle method en_US
dc.subject IPH functions en_US
dc.subject Zak transform en_US
dc.subject BMO en_US
dc.subject Modulation spaces en_US
dc.subject.lcsh Moduli theory
dc.subject.lcsh Transformations (Mathematics)
dc.subject.lcsh Gabor transforms
dc.subject.lcsh Mathematical optimization
dc.subject.lcsh Spaces of homogeneous type
dc.title Modulation spaces, BMO and the Zak transform, and minimizing IPH functions over the unit simplex en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Heil, Christopher E.
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isAdvisorOfPublication 028e721e-4900-46cd-b15d-55567896904f
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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