Given a finite group $G$, we examine the classification of all frame representations of $G$ and the classification of all $G$-frames, \emph{i.e.,} frames induced by group representations of $G$. We show that the exact number of equivalence classes of $G$-frames and the exact number of frame representations can be explicitly calculated. We also discuss how to calculate the largest number $L$ such that there exists an $L$-tuple of strongly disjoint $G$-frames.

Keywords:

frames, group-frames, frame representations, disjoint frames frames, group-frames, frame representations, disjoint frames

MSC Classifications:

42C15, 46C05, 47B10 show english descriptions General harmonic expansions, frames
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 42C15 - General harmonic expansions, frames
46C05 - Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
47B10 - Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]

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