论文标题
自相关线性关系和对广义nevanlinna函数的应用可降低
Reducibility of self-adjoint linear relations and application to generalized Nevanlinna functions
论文作者
论文摘要
给出了在孔林空间中自我接触线性关系可降低必要和充分的条件。然后，由自我接合线性关系$ a $表示的广义nevanlinna函数$ q $通过减少$ a $的减少子空间进行分解。两个函数的总和$ q_ {i} {\ in n} _ {κ_{κ_{i}} \ left（\ Mathcal {h} \ right），\ thinspace i = 1，\ thinspace 2 $，由Triplets $ \ left（还研究了\ Mathcal {k} _ {i}，a_ {i}，γ_{i} \ right）$。为此，模型$（\ tilde {\ tilde {k}}，\ tilde {a}，\ tilde {γ}）$表示$ q：= q_ {1}+q_ {1}+q_ {2} $ of $ \ weft（\ nath） \ right）$是创建的。通过该模型，用分析术语证明了$κ=κ_{1}+κ_{2} $的必要条件和足够条件。最后，解释了代表关系$ a $的退化约旦链如何影响减少$ a $的子空间和相应函数$ q $的分解。
Necessary and sufficient conditions for reducidibility of a self-adjoint linear relation in a Krein space are given. Then a generalized Nevanlinna function $Q$, represented by a self-adjoint linear relation $A$, is decomposed by means of the reducing subspaces of $A$. The sum of two functions $Q_{i}{\in N}_{κ_{i}}\left( \mathcal{H} \right),\thinspace i=1,\thinspace 2$, minimally represented by the triplets $\left( \mathcal{K}_{i},A_{i},Γ_{i} \right)$, is also studied. For that purpose, a model $( \tilde{\mathcal{K}},\tilde{A},\tilde{Γ} )$ to represent $Q:=Q_{1}+Q_{2}$ in terms of $\left( \mathcal{K}_{i},A_{i},Γ_{i} \right)$ is created. By means of that model, necessary and sufficient conditions for $κ=κ_{1}+κ_{2}$ are proven in analytic terms. At the end, it is explained how degenerate Jordan chains of the representing relation $A$ affect reducing subspaces of $A$ and decomposition of the corresponding function $Q$.
