Geodesic
The L. de Branges spaces and functional models of non-dissipative operators
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 4, pp. 622-641 Cet article a éte moissonné depuis la source Math-Net.Ru

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The functional model for any bounded non-dissipative operator $A$ in Hilbert space $H$ with $\operatorname{rank}\Bigl(\dfrac{A-A^*}i\Bigr)=2$ has been constructed. This model is realized by the operator of multiplication on independent variable in the L. de Branges space of holomorphic functions. In difference with the L. de Branges space of entire functions the spaces of holomorphic in $\mathbb C$ functions with predefined singularities on the real axis have been studied. This allowed to construct the functional models for non-dissipative operators with real spectrum when $\operatorname{rank}\Bigl(\dfrac{A-A^*}i\Bigr)=2$. 
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     author = {V. A. Zolotarev},
     title = {The {L.~de~Branges} spaces and functional models of~non-dissipative operators},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
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V. A. Zolotarev. The L. de Branges spaces and functional models of non-dissipative operators. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 4, pp. 622-641. http://geodesic.mathdoc.fr/item/JMAG_2002_9_4_a5/