Absolutely continuous spectrum of fourth order difference operators with unbounded coefficients on a Hilbert space

Master's Thesis from the year 2015 in the subject Mathematics - Analysis, grade: A, , course: MSC Pure mathematics, language: English, abstract: In this study, the author has investigated the absolutely continuous spectrum of a fourth order self-adjoint extension operator of minimal operator generated by difference equation defined on a weighted Hilbert space with the weight function w(t) > 0, t ? N where p(t), q(t), r(t) and m(t) are real-valued functions. The author has applied the M-matrix theory as developed in Hinton and Shaw in order to compute the spectral multiplicity and the location of the absolutely continuous spectrum of self-adjoint extension operator. These results have been an extension of some known spectral results of fourth order differential operators to difference setting. Similarly, they have extended results found in Jacobi matrices. In this thesis, chapter 1 is about introduction and some preliminary results including literature review, objectives, methodology and basic definitions. In chapter 2, the author has given the results on the computation of the eigenvalues, dichotomy conditions and some results on singular continuous spectrum. Chapter 3 contains the main results in deficiency indices, absolutely continuous spectrum and the spectral multiplicity. Finally, the author has summarized his results in chapter 4 and also highlighted areas of further research.

Evans Mogoi is currently a Lecturer and head of Mathematics at Eregi Teachers Training College and also a part-time Lecturer of Pure Mathematics at Alupe university, University of Nairobi,Kisii University and Mount Kenya University.Evans holds masters degree (MSC in pure Mathematics) from Maseno University, a bachelors degree (BED Sciences) from Kampala International University, and a Diploma in Education Sciences from Kagumo Teachers Training College. His interests include training Mathematics teachers,Engineers and all other professionals that require Mathematics skills.He has developed (ALP) Active Learning Program used in classroom when teaching Mathematics and won the Lecturer Awards from Eregi Teachers Training College and also from the University of Amsterdam(Netherlands) in 2015 and 2017 respectively.