Full Length Research Paper
Abstract
In this paper, we study continuous frames in Hilbert spaces using a family of linearly independent vectors called coherent state (CS) and applying it in any physical space. To accomplish this goal, the standard theory of frames in Hilbert spaces, using discrete bases, is generalized to one where the basis vectors may be labeled using discrete, continuous or a mixture of the two types of indices. A comprehensive analysis of such frames is presented and illustrated by the examples drawn from a toy example Sea Star and the affine group.
Key words: Frame, continuous frame, unitary representation, coherent state (CS), sea star, affine group.
Copyright © 2024 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0