Three-term recurrence relations with matrix coefficients. The completely indefinite caseстатья
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Аннотация:In the space {ol p 2 of vector sequences, we consider the symmetric operatorL generated by the expression (lu)j:=Bj uj+1+Aj uj+ B j−1/*uj−1, whereu−1 = 0,u 0,u 1, … ∈ ℂ p ,A j andB j arep × p matrices with entries from ℂ,A j *=Aj, and the inversesB j −1 (j = 0, 1, …) exist. We state a necessary and sufficient condition for the deficiency numbers of the operatorL to be maximal; this corresponds to the completely indefinite case for the expressionl. Tests for incomplete indefiniteness and complete indefiniteness forl in terms of the coefficientsA j andB j are derived.