English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let $A$ be a densely defined simple symmetric operator in $\gH$, let$\Pi=\bt$ be a boundary triplet for $A^*$ and let $M(\cd)$ be the correspondingWeyl function. It is known that the Weyl function $M(\cd)$ determines theboundary triplet $\Pi$, in particular, the pair ${A,A_0}$, where $A_0:=A^*\lceil\ker\G_0 (= A^*_0)$, uniquely up to unitary similarity. At the sametime the Weyl function corresponding to a boundary triplet for a dual pair ofoperators defines it uniquely only up to weak similarity.  In this paper we consider symmetric dual pairs ${A,A}$ generated by $A\subsetA^*$ and special boundary triplets $\wt\Pi$ for ${A,A}$. We are interestedwhether the result on unitary similarity remains valid provided that the Weylfunction corresponding to $\wt\Pi$ is $\wt M(z)= K^*(B-M(z))^{-1} K,$ where $B$is some non-self-adjoint bounded operator in $\cH$. We specify some conditionsin terms of the operators $A_0$ and $A_B= A^*\lceil \ker(\G_1-B\G_0)$, whichdetermine uniquely (up to unitary equivalence) the pair ${A,A_B}$ by the Weylfunction $\wt M(\cd)$. Moreover, it is shown that under some additionalassumptions the Weyl function $M_\Pi(\cdot)$ of the boundary triplet $\Pi$ forthe dual pair $\DA$ determines the triplet $\Pi$ uniquely up to unitarysimilarity. We obtain also some negative results demonstrating that in generalthe Weyl function $\wt M(\cd)$ does not determine the operator $A_B$ even up tosimilarity.

Unitary equivalence of proper extensions of a symmetric operator and the Weyl function