Some inequalities for Parseval frames (Q6550064)

This paper explores the angles between vectors of Parseval frames, presenting various inequalities related to these angles and examining the conditions under which vectors of Parseval frames become orthogonal. Additionally, it reviews key properties associated with Parseval frames and provides examples to illustrate these concepts. The authors further investigate a strong inequality involving the angles between vectors in Parseval frames and explore different conditions for equality. The existence of Parseval frames under certain conditions is also analyzed. Finally, the paper discusses the distance between vectors in Parseval frames, deriving several inequalities in relation to this distance.\N\NFor the entire collection see [Zbl 1531.35008].