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首页> 外文期刊>Journal of Mathematical Physics, Analysis, Geometry >On the Universal Models of Commutative Systems of Linear Operators
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On the Universal Models of Commutative Systems of Linear Operators

机译:线性算子交换系统的通用模型

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The universal models are constructed for a system of linear bounded non-selfadjoint operators { A 1, A 2} acting in a Hilbert space H such that 1) [ A 1, A 2] = 0, [ A 1*, A 2] = 0; 2) ≥ 0 ( k = 1, 2); 3) the function A ( l ) = A 1 ( l 1) A 2 ( l 2) ( A k ( l k ) = A k ( I - l k Ak )-1, k = 1, 2) is an entire function of the exponential type. It is proved that this class of linear operator systems is realized by the restriction on invariant subspaces of systems of operator of integration by independent variables in L 2( W -) ? - l 2 where - W - is a rectangle in R 2.
机译:通用模型是针对在希尔伯特空间H中作用为1)的线性有界非自伴算子{A 1 ,A 2 }的系统构造的> 1 ,A 2 ] = 0,[A 1 *,A 2 ] = 0; 2)≥0(k = 1,2); 3)函数A(l)= A 1 (l 1 )A 2 (l 2 )( A k (l k )= A k (I-l k A k -1 ,k = 1,2)是指数类型的整个函数。证明了这类线性算子系统是由L 2 (W-)?中的自变量对积分算子的系统不变子空间的限制而实现的。 -l 2 其中-W-是R 2 中的矩形。

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