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Deficiency indices and spectrum of fourth order difference equations with unbounded coefficients |
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| Authors: | John Ogonji Agure David Otieno Ambogo Fredrick Oluoch Nyamwala |
| Institution: | 1. School of Mathematics, Applied Statistics & Actuarial Science, Maseno University, Box 333 Maseno, KenyaPhone: +254 721 271 122, Fax: +254 57 351221;2. School of Mathematics, Applied Statistics & Actuarial Science, Maseno University, Box 333 Maseno, KenyaPhone: +254 723 843 943, Fax: +254 57 351221;3. School of Mathematics, Applied Statistics & Actuarial Science, Maseno University, Box 333 Maseno, Kenya |
| Abstract: | Using subspace theory together with appropriate smoothness and decay conditions, we calculated the deficiency indices and absolutely continuous spectrum of fourth order difference equations with unbounded coefficients. In particular, we found the absolutely continuous spectrum to be ${\mathbb {R}}$ with a spectral multiplicity one. |
| Keywords: | Eigenvalues deficiency indices absolutely continuous spectrum MSC (2010) Primary: 39A20 Secondary: 47A55 |