Deficiency Indices and Spectra of Fourth Order Differential Operators with Unbounded Coeffcients on a Hilbert Space

Master’s Thesis from the year 2016 in the subject Mathematics - Algebra, language: English, abstract: In this thesis, using asymptotic integration, we have investigated the asymptotic of the eigensolutions 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. We have mainly endeavored 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 the self-adjoint extension operator together with their spectral multiplicity. Results obtained for deficiency indices were in the range (2, 2)