dc.contributor.advisor Deeter, Charles R. dc.contributor.author Berzsenyi, George en_US dc.date.accessioned 2019-10-11T15:11:01Z dc.date.available 2019-10-11T15:11:01Z dc.date.created 1969 en_US dc.date.issued 1969 en_US dc.identifier aleph-236358 en_US dc.identifier.uri https://repository.tcu.edu/handle/116099117/33803 dc.description.abstract The aim of this paper is to further the theory of monodiffric functions introduced by R. P. Isaacs (A Finite Difference Function Theory, Universidad Nacional Tucuman Revista, vol. 2 (1941), pp. 177-201). Besides developing the concept of monodiffric duality and solving an important boundary-value problem, several new methods of integration are presented. Interrelations among these line integrals are analyzed, and analogs are given for Cauchy's Integral Formula for the Derivative and the method of Integration by Parts. Convolution products of monodiffric functions are derived and analyzed both from the algebraic and from the function-theoretic viewpoint . One of these convolution products is then used to define a product operation for monodiffric functions. It-is shown that the class of functions monodiffric in the first quadrant of the discrete plane forms a commutative integral domain with identity with respect to pointwise addition and the product operation defined. It is also shown that the pseudo-powers of z satisfy the law of exponents with respect to this product operation. dc.format.extent iii, 55 leaves, bound en_US dc.format.medium Format: Print en_US dc.language.iso eng en_US dc.relation.ispartof Texas Christian University dissertation en_US dc.relation.ispartof AS38.B478 en_US dc.subject.lcsh Holomorphic functions en_US dc.title Products of monodiffric functions en_US dc.type Text en_US etd.degree.department Department of Mathematics etd.degree.level Doctoral local.college College of Science and Engineering local.department Mathematics local.academicunit Department of Mathematics dc.type.genre Dissertation local.subjectarea Mathematics dc.identifier.callnumber Main Stacks: AS38 .B478 (Regular Loan) dc.identifier.callnumber Special Collections: AS38 .B478 (Non-Circulating) etd.degree.name Doctor of Philosophy etd.degree.grantor Texas Christian University
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