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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For a matrix-valued function $\Phi\in L^2_{M_{n\times m}}$, it is well-knownthat the kernel of a block Hankel operator $H_\Phi$ is an invariant subspacefor the shift operator. Thus, if the kernel is nontrivial, then $\ker H_\Phi=\Theta H^2_{\mathbb C^r}$ for a natural number $r$ and an $m\times r$ matrixinner function $\Theta$ by Beurling-Lax-Halmos Theorem. It will be shown thatthe size of the matrix inner function $\Theta$ associated with the kernel of ablock Hankel operator $H_\Phi$ is closely related with a certain independencyof the columns of $\Phi$, which is defined in this paper. As an importantapplication of this result, the shape of shift invariant, or, backward shiftinvariant subspaces of $H^2_{\mathbb C^n}$ generated by finite elements will bestudied.

Kernels of block Hankel operators and independency of vector-valued functions modulo Nevanlinna class