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dc.contributor.advisorDeeter, Charles R.
dc.contributor.authorBolen, James Cordellen_US
dc.description.abstractIn 1944, J. Ferrand introduced the concept of a discrete analytic function. Many properties of discrete analytic functions were developed by R. J. Duffin in 1956. In the first part of this dissertation a reproducing kernel is defined and is shown to have analogous properties of the Bergman kernel for analytic functions. The next part of the paper discusses various types of convergence of discrete analytic functions to a given analytic function defined on a simply connected domain, Finally, it is shown that it is not reasonable to expect the discrete kernels to converge to the Bergman kernel defined on a simply connected domain.
dc.format.extentiii, 54 leaves, bounden_US
dc.format.mediumFormat: Printen_US
dc.relation.ispartofTexas Christian University dissertationen_US
dc.subject.lcshAnalytic functionsen_US
dc.subject.lcshKernel functionsen_US
dc.titleA reproducing kernel function and convergence properties for discrete analytic functionsen_US
dc.typeTexten_US of Mathematics
local.collegeCollege of Science and Engineering
local.academicunitDepartment of Mathematics
dc.identifier.callnumberMain Stacks: AS38 .B65 (Regular Loan)
dc.identifier.callnumberSpecial Collections: AS38 .B65 (Non-Circulating) of Philosophy Christian University

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