Essential and continuous spectrum of symmetric difference equations

Abstract

Essential and continuous spectrum of symmetric difference equations have been inves- tigated. It has been shown that the deficiency indices and the existence of these com- ponents 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 condi- tions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation.