Article
Kyungpook Mathematical Journal 2020; 60(2): 297-305
Published online June 30, 2020
Copyright © Kyungpook Mathematical Journal.
Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient
Fredrick Oluoch Nyamwala∗, David Otieno Ambogo, Joyce Mukhwana Ngala
Department of Mathematics, Moi University, 3900-30100, Eldoret, Kenya
e-mail : foluoch2000@yahoo.com or foluoch2000@mu.ac.ke
Department of Pure and Applied Mathematics, Maseno University, 333-40105, Maseno, Kenya
e-mail : otivoe@yahoo.com
Department of Mathematics, Moi University, 3900-30100, Eldoret, Kenya
e-mail : mukhwana.ngala@gmail.com
Received: February 20, 2019; Revised: April 21, 2020; Accepted: April 22, 2020
We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.
Keywords: differential operators, selfadjoint realisations, deficiency indices, spectrum