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Absolutely Continuous Spectrum of fourth Order Di_erence Operators With unbounded Coe_cients on the Hilbert space `2(N)

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dc.contributor.author MOGOI, Evans N.
dc.date.accessioned 2019-01-23T06:51:37Z
dc.date.available 2019-01-23T06:51:37Z
dc.date.issued 2015
dc.identifier.uri https://repository.maseno.ac.ke/handle/123456789/1057
dc.description PHD Thesis en_US
dc.description.abstract Sturm-Liouville operators and Jacobi matrices have so far been developed in parallel for many years. A result in one _eld usually leads to a result in the other. However not much in terms of spectral theory has been done in the discrete setting compared to the continuous version especially in higher order operators. Thus, we have investigated the de_ciency indices of fourth order di_erence operator generated by a fourth order di_erence equation and located the absolutely continuous spectrum of its self-adjoint extension as well as the spectral multiplicity using the M-matrix. The results are useful to mathematicians and can be applied in quantum mechanics to calculate time dilation and length contraction as used in Lorentz-Fotzgeralds transformations. The study has been carried out through asymptotic summation as outlined in Levinson Benzaid Lutz-theorem. This involved: reduction of a fourth order di_erence equation into _rst order, computation of the eigenvalues, proof of uniform dichotomy condition, calculating the de_ciency indices and locating absolutely continuous spectrum. In this case we have found the absolutely continuous spectrum to be the whole set of real numbers of spectral multiplicity one. en_US
dc.language.iso en_US en_US
dc.publisher Maseno University en_US
dc.subject Pure and applied Mathematics en_US
dc.title Absolutely Continuous Spectrum of fourth Order Di_erence Operators With unbounded Coe_cients on the Hilbert space `2(N) en_US
dc.type Thesis en_US


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