Three-term recurrence relations with matrix coefficients. The completely indefinite case

被引:25
作者
Kostyuchenko, AG
Mirzoev, KA
机构
[1] Moscow MV Lomonosov State Univ, Moscow 117234, Russia
[2] KE Tsiolkovskii Moscow Aviat Technol Inst, Moscow, Russia
关键词
sequence space; difference expression; matrix polynomial; deficiency numbers of an operator;
D O I
10.1007/BF02312843
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In the space l(p)(2) of vector sequences, we consider the symmetric operator L generated by the expression (lu)(j) := B(j)u(j+1) + A(j)u(j) + Bj-1*u(j-1), where u(-1) = 0, u(0), u(1), ... is an element of C-p, A(j) and B-j are p x p matrices with entries from C, A(j)* = A(j), and the inverses B-j(-1) (j = 0, 1,...) exist. We state a necessary and sufficient condition for the deficiency numbers of the operator L to be maximal; this corresponds to the completely indefinite case for the expression I. Tests for incomplete indefiniteness and complete indefiniteness for l in terms of the coefficients A(j) and B-j are derived.
引用
收藏
页码:624 / 630
页数:7
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