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

Operator-valued frame ($G$-frame), as a generalization of frame is introducedby Kaftal, Larson, and Zhang in \textit{Trans. Amer. Math. Soc.},361(12):6349-6385, 2009 and by Sun in \textit{J. Math. Anal. Appl.},322(1):437-452, 2006. It has been further extended in the paperarXiv:1810.01629 [math.OA] 3 October 2018, so as to have a rich theory onoperator-valued frames for Hilbert spaces as well as for Banach spaces. Thecontinuous version has been studied in this paper when the indexing set is ameasure space. We study duality, similarity, orthogonality and stability ofthis extension. Several characterizations are given including a notablecharacterization when the measure space is a locally compact group. Variationformula, dimension formula and trace formula are derived when the Hilbert spaceis finite dimensional.

Extension of frames and bases -- II