A fundamental identity for Parseval frames
R. Balan, P.G. Casazza, D. Edidin, G. Kutyniok
TL;DR
This paper introduces a surprising fundamental identity for Parseval frames in Hilbert spaces, extending it to general frames and discussing its implications.
Contribution
It presents a novel fundamental identity for Parseval frames and generalizes it to broader frame classes.
Findings
New fundamental identity for Parseval frames
Extensions to general frames
Discussion of theoretical implications
Abstract
In this paper we establish a suprising fundamental identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Numerical Analysis Techniques · Digital Filter Design and Implementation