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Analysis of Conjugate Harmonic Components of Monogenic Functions and Lambda Harmonic Functions

Title: An Analysis of Conjugate Harmonic Components of Monogenic Functions and Lambda Harmonic Functions.
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Name(s): Ballenger-Fazzone, Brendon Kerr, author
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
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2016
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (89 pages)
Language(s): English
Abstract/Description: 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.
Identifier: FSU_2016SP_BallengerFazzone_fsu_0071E_13136 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Spring Semester 2016.
Date of Defense: April 11, 2016.
Keywords: Clifford analysis, Harmonic analysis, Monogenic functions
Bibliography Note: Includes bibliographical references.
Advisory Committee: 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.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_2016SP_BallengerFazzone_fsu_0071E_13136
Owner Institution: FSU

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Ballenger-Fazzone, B. K. (2016). An Analysis of Conjugate Harmonic Components of Monogenic Functions and Lambda Harmonic Functions. Retrieved from http://purl.flvc.org/fsu/fd/FSU_2016SP_BallengerFazzone_fsu_0071E_13136