Aulbach, Bernd; Nguyen Van Minh The concept of spectral dichotomy for linear difference equations. II. (English) Zbl 0880.39009 J. Difference Equ. Appl. 2, No. 3, 251-262 (1996). The authors extend their previous results [J. Math. Anal. Appl. 185, No. 2, 275-287 (1994; Zbl 0806.39005)] on the equivalence of the spectral dichotomy and the well-known exponential dichotomy to the class of linear difference equations whose right-hand sides are not necessarily invertible. Further they establish necessary and sufficient conditions for exponential and uniform stability for equations on the set of positive integers. Reviewer: E.Thandapani (Salem) Cited in 2 ReviewsCited in 39 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis Keywords:spectral dichotomy; exponential dichotomy; linear difference equations; exponential and uniform stability Citations:Zbl 0806.39005 PDF BibTeX XML Cite \textit{B. Aulbach} and \textit{Nguyen Van Minh}, J. Difference Equ. Appl. 2, No. 3, 251--262 (1996; Zbl 0880.39009) Full Text: DOI OpenURL References: [1] DOI: 10.1016/0022-247X(85)90243-4 · Zbl 0595.34060 [2] DOI: 10.1006/jmaa.1994.1248 · Zbl 0806.39005 [3] DOI: 10.1142/9789812796417_0004 [4] Daleckii Ju.L., Translations, Amer. Math. Soc., R.I. 4 (1974) [5] Dunford N., Linear Operators I, General Theory (1958) · Zbl 0088.32102 [6] Henry D., Lecture Notes in Mathematics 840 (1981) [7] DOI: 10.1006/jmaa.1994.1360 · Zbl 0811.34064 [8] Sljusarchuk V.E., Ukrain. Mat. Zh. 35 pp 109– (1983) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.