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

Mogoi, Evans

ISBN 10: 3659742872 / ISBN 13: 9783659742873

Editore: LAP LAMBERT Academic Publishing, 2017

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• Titolo: Spectral theory of difference operators: Absolutely continuous spectrum of fourth order difference operators with unbounded coefficients on a Hilbert space
• Editore: LAP LAMBERT Academic Publishing
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 3659742872
• ISBN 13: 9783659742873
• Rilegatura: Brossura
• Condizione: New

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Riassunto

Sturm-Liouville operators and Jacobi matrices have so far been developed in parallel for many years. 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 deficiency indices of fourth order difference operator generated by a fourth order difference 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 difference equation into first order, computation of the eigenvalues, proof of uniform dichotomy condition, calculating the deficiency 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.

Informazioni sull?autore

Mogoi N. Evans is a mathematics instructor at Eregi Teachers Training College. He studied Mathematics and Physics at Kampala International University and holds MSC degree in Pure Mathematics from Maseno University.He also studied Mathematics and Physics at Kagumo Teachers College. He is currently a part-time lecturer in the university of Nairobi.