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De ciency indices and spectra of Fourth order Di erential Operators with Unbounded Coe cients on a Hilbert space

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dc.contributor.author ACHIANDO, Rodgers Onyango
dc.date.accessioned 2019-01-23T08:14:36Z
dc.date.available 2019-01-23T08:14:36Z
dc.date.issued 2016
dc.identifier.uri https://repository.maseno.ac.ke/handle/123456789/1073
dc.description Masters' Thesis en_US
dc.description.abstract The concept of unbounded operators provides an abstract framework for dealing with differential operators and unbounded observable such as in quantum mechanics. The theory of unbounded operators was developed by John Von Neumann in the late 1920s and early 1930s in an effort to solve quantum mechanics and other physical observables. This has provided the background on which other scholars have developed their work in differential operators. Higher order differential operators as defined on Hilbert spaces have received much attention though there still lies the problem of computing the eigenvalues of these higher order operators when the coefficients are unbounded. Using asymptotic integration, we have investigated the asymptotics of the eigenvalues and the deficiency indices of fourth-order differential operators with unbounded coefficients as well as the location of absolutely continuous spectrum of self-adjoint extension operators. The objectives of this research were to compute eigenvalues of fourth order differential operators when the coefficients are unbounded, determine the deficiency indices of such differential operator and the location of the absolutely continuous spectrum of self-adjoint extension operator together with their spectral multiplicity. These results have enriched the available literature on the spectral theory of higher order differential operators and can also be applicable in quantum mechanics where results of self-adjoint operators are very much useful. In solving these problems, we applied the techniques of asymptotic integration as outlined in Levinson’s theorem which is a perturbation result. en_US
dc.language.iso en_US en_US
dc.publisher Maseno University en_US
dc.subject Differential operators en_US
dc.title De ciency indices and spectra of Fourth order Di erential Operators with Unbounded Coe cients on a Hilbert space en_US
dc.type Thesis en_US


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