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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The concept of canonical dual - Bessel sequences was recently introduced, a deep study of which is helpful in further developing and enriching the duality theory of - frames. In this paper we pay attention to investigating the structure of the canonical dual - Bessel sequence of a Parseval - frame and some derived properties. We present the exact form of the canonical dual - Bessel sequence of a Parseval - frame, and a necessary and sufficient condition for a dual - Bessel sequence of a given Parseval - frame to be the canonical dual - Bessel sequence is investigated. We also give a necessary and sufficient condition for a Parseval - frame to have a unique dual - Bessel sequence and equivalently characterize the condition under which the canonical dual - Bessel sequence of a Parseval - frame admits a unique dual - Bessel sequence. Finally, we obtain a minimal norm property on expansion coefficients of elements in the range of resulting from the canonical dual - Bessel sequence of a Parseval - frame.

journal of function spaces

Some Properties of Canonical Dual <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:math>-Bessel Sequences for Parseval <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:math>-Frames

Some Properties of Canonical Dual K-Bessel Sequences for Parseval K-Frames