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

We consider the multidimensional Borg-Levinson theorem of determining boththe magnetic field $dA$ and the electric potential $V$, appearing in theDirichlet realization of the magnetic Schr\"odinger operator $H=(-{\rmi}\nabla+A)^2+V$ on a bounded domain $\Omega\subset\mathbb R^n$, $n\geq2$, frompartial knowledge of the boundary spectral data of $H$. The full boundaryspectral data are given by the set $\{(\lambda_{k},{\partial_\nu\phi_{k}}_{|\partial\Omega}):\ k\geq1\}$, where $\{ \lambda_k:\ k\in \mathbbN^* \}$ is the non-decreasing sequence of eigenvalues of $H$, $\{ \phi_k:\ k\in\mathbb N^* \}$ an associated Hilbertian basis of eigenfunctions and $\nu$ isthe unit outward normal vector to $\partial\Omega$. We prove that someasymptotic knowledge of $(\lambda_{k},{\partial_\nu\phi_{k}}_{|\partial\Omega})$ with respect to $k\geq1$ determines uniquely themagnetic field $dA$ and the electric potential $V$.

A multidimensional Borg-Levinson theorem for magnetic Schr\"odinger operators with partial spectral data