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Deficiency indices and spectrum of fourth order difference equations with unbounded coefficients
Author(s) -
Agure John Ogonji,
Ambogo David Otieno,
Nyamwala Fredrick Oluoch
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200161
Subject(s) - mathematics , multiplicity (mathematics) , smoothness , spectrum (functional analysis) , subspace topology , absolute continuity , mathematical analysis , order (exchange) , pure mathematics , mathematical physics , physics , quantum mechanics , finance , economics
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 \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {R}}$\end{document} with a spectral multiplicity one.