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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We propose a method for the spectral analysis of unbounded operator matricesin a general setting which fully abstains from standard perturbative arguments.Rather than requiring the matrix to act in a Hilbert space $\mathcal{H}$, weextend its action to a suitable distributional triple $\mathcal{D} \subset\mathcal{H} \subset \mathcal{D}_-$ and restrict it to its maximal domain in$\mathcal{H}$. The crucial point in our approach is the choice of the spaces$\mathcal{D}$ and $\mathcal{D}_-$ which are essentially determined by the Schurcomplement of the matrix. We show spectral equivalence between the resultingoperator matrix in $\mathcal{H}$ and its Schur complement, which allows to passfrom a suitable representation of the Schur complement (e.g. by generalisedform methods) to a representation of the operator matrix. We thereby generaliseclassical spectral equivalence results imposing standard dominance patterns.  The abstract results are applied to damped wave equations with possiblyunbounded and/or singular damping, to Dirac operators with Coulomb-typepotentials, as well as to generic second order matrix differential operators.By means of our methods, previous regularity assumptions can be weakenedsubstantially.

Schur complement dominant operator matrices