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Essential and continuous spectrum of symmetric difference equations

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  • Fredrick Oluoch Nyamwala

Abstract

Essential and continuous spectrum of symmetric difference equations have been investigated. It has been shown that the deficiency indices and the existence of these components of the spectrum are determined by the growth conditions of the coefficients. In particular, the deficiency indices are superimposition of those clusters determined by the coefficient growth. Finally, we have proved the neccessary and sufficient conditions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation.

Suggested Citation

  • Fredrick Oluoch Nyamwala, 2017. "Essential and continuous spectrum of symmetric difference equations," Mathematische Nachrichten, Wiley Blackwell, vol. 290(17-18), pages 2977-2991, December.
    • Handle: RePEc:bla:mathna:v:290:y:2017:i:17-18:p:2977-2991
    DOI: 10.1002/mana.201600183
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