Abstract
The concept of unbounded operators provides an abstract framework for
dealing with dierential 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 eort
to solve problems related to quantum mechanics and other physical ob-
servables. This has provided the background on which other scholars
have developed their work in dierential operators. Higher order dieren-
tial operators as dened on Hilbert spaces have received much attention
though there still lies the problem of computing the eigenvalues of these
higher order operators when the coecients are unbounded. In this the-
sis,using asymptotic integration, we have investigated the asymptotics of
the eigensolutions and the deciency indices of fourth order dierential
operators with unbounded coecients as well as the location of absolutely
continuous spectrum of self-adjoint extension operators. We have mainly
endeavuored to compute eigenvalues of fourth order dierential operators
when the coecients are unbounded, determine the deciency indices of
such dierential operator and the location of the absolutely continuous
spectrum of the self-adjoint extension operator together with their spec-
tral multiplicity. Results obtained for deciency indices was in the range
(2; 2) defT (4; 4) under dierent growth and decay conditions of co-
ecients. In addition, the absolutely continuous spectrum is either half
or full line of spectral multiplicity 1 or 2 depending on the integrability
ONYANGO, A (2021). De ciency indices and spectra of Fourth order Differential Operators with Unbounded Coefficients on a Hilbert space. Afribary. Retrieved from https://tracking.afribary.com/works/de-ciency-indices-and-spectra-of-fourth-order-differential-operators-with-unbounded-coefficients-on-a-hilbert-space
ONYANGO, ACHIANDO "De ciency indices and spectra of Fourth order Differential Operators with Unbounded Coefficients on a Hilbert space" Afribary. Afribary, 07 May. 2021, https://tracking.afribary.com/works/de-ciency-indices-and-spectra-of-fourth-order-differential-operators-with-unbounded-coefficients-on-a-hilbert-space. Accessed 24 Nov. 2024.
ONYANGO, ACHIANDO . "De ciency indices and spectra of Fourth order Differential Operators with Unbounded Coefficients on a Hilbert space". Afribary, Afribary, 07 May. 2021. Web. 24 Nov. 2024. < https://tracking.afribary.com/works/de-ciency-indices-and-spectra-of-fourth-order-differential-operators-with-unbounded-coefficients-on-a-hilbert-space >.
ONYANGO, ACHIANDO . "De ciency indices and spectra of Fourth order Differential Operators with Unbounded Coefficients on a Hilbert space" Afribary (2021). Accessed November 24, 2024. https://tracking.afribary.com/works/de-ciency-indices-and-spectra-of-fourth-order-differential-operators-with-unbounded-coefficients-on-a-hilbert-space