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.  
Highlights
The Hilbert space is the natural framework for the mathematical description of many areas of Physics and Mathematics
Mathematical formulation of frames in H was discussed by taking the famous articles by Ali et al, (1993) and Rahimi et al, (2017)
If we introduce the positive operator: n
Summary
The uniqueness of the decomposition and the orthogonality of the basis vectors, while maintaining its others useful properties: fast convergence, numerical stability of the reconstruction n , etc. The resulting object is called a discrete frame, a concept introduced by Duffin and Schaeffer (1952) in the context of non-harmonic Fourier analysis. Latter the concept of generalization of frames was proposed by Daubechies et al (1986) and independently by Ali et al, (1993). Is called dual or reciprocal frame, with frame bounds B 1 , A 1. Analogy with a tight frame is clear and it seems natural to call the set of vectors g , g G a continuous tight frame. Continuous frames in Hilbert space were studied and applied to any physical space
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