New inequalities for weaving frames in Hilbert spaces

TL;DR

This paper introduces new inequalities and identities for weaving frames in Hilbert spaces, generalizing previous results and involving scalar parameters to enhance the theoretical framework of frame analysis.

Contribution

It presents novel inequalities and identities for weaving frames, extending prior work by incorporating scalar parameters and broadening the theoretical understanding.

Findings

Established Parseval identities for weaving frames

Derived new inequalities involving scalar parameters

Generalized previous results by Balan et al. and G32vru36a

Abstract

In this paper, we establish Parseval identities and surprising new inequalities for weaving frames in Hilbert space, which involve scalar $\lambda\in\rs$. By suitable choices of $\lambda$, one obtains the previous results as special cases. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and G\u{a}vru\c{t}a.