Clifford analysis is seen as the higher dimensional analogue of complex analysis. This includes a rich study of Clifford
algebras and, in particular, monogenic functions, or Clifford-valued functions that lie in the kernel of the Cauchy-Riemann operator. In
this dissertation, we explore the relationships between the harmonic components of monogenic functions and expand upon the notion of
conjugate harmonic functions. We show that properties of the even part of a Clifford-valued function determine properties of the odd part
and vice versa. We also explore the theory of functions lying in the kernel of a generalized Laplace operator, the λ-Laplacian. We explore
the properties of these so-called λ-harmonic functions and give the solution to the Dirichlet problem for the λ-harmonic functions on
annular domains in Rⁿ. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements
for the degree of Doctor of Philosophy. / Spring Semester 2016. / April 11, 2016. / Clifford analysis, Harmonic analysis, Monogenic functions / Includes bibliographical references. / Craig A. Nolder, Professor Directing Thesis; Kristine C. Harper, University Representative;
Ettore Aldrovandi, Committee Member; Bettye Anne Case, Committee Member; John R. Quine, Committee Member; John Ryan, Committee
Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_360317 |
| Contributors | Ballenger-Fazzone, Brendon Kerr (authoraut), Nolder, Craig (professor directing thesis), Harper, Kristine (university representative), Aldrovandi, Ettore (committee member), Case, Bettye Anne (committee member), Quine, J. R. (John R.) (committee member), Ryan, John Barry (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting department) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (89 pages), computer, application/pdf |
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