@article{Borogovac_2022, title={Reducibility of self-adjoint linear relations and application to generalized Nevanlinna functions}, volume={74}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6084}, DOI={10.37863/umzh.v74i7.6084}, abstractNote={<pre>UDC 517.9<br>We present necessary and sufficient conditions for the reducibility of a self-adjoint linear <br>relation in a Krein space. <br>Then a generalized Nevanlinna function $Q$ represented by a self-adjoint linear <br>relation $A$ in a Pontryagin space is decomposed by means of the reducing subspaces of $A.$ <br>The sum of two functions $Q_{i}{\in N}_{\kappa_{i }(\mathcal{H}),$ $i=1, 2,$ minimally <br>represented by the triplets $(\mathcal{K}_{i},A_{i},\Gamma_{i})$ is also studied. <br>For this purpose, we create a model $(\tilde{\mathcal{K },\tilde{A},\tilde{\Gamma })$ to <br>represent $Q:=Q_{1}+Q_{2}$ in terms of $(\mathcal{K}_{i},A_{i},\Gamma_{i})$. <br>By using this model, necessary and sufficient conditions for $\kappa =\kappa_{1}+\kappa_{2}$ are proved in the analytic form. <br>Finally, we explain how degenerate Jordan chains of the representing relation $A$ affect the reducing subspaces of $A$ and the <br>decomposition of the corresponding function $Q.$</pre>}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Borogovac,M. }, year={2022}, month={Aug.}, pages={893 - 920} }