For a connected reductive group $G$ defined over $\mathbb{F}_q$ and equipped with the induced Frobenius endomorphism $F$, we study relation among following three $\mathbb{Z}$-algebras: (i) $\mathbb{Z}$-model $\mathsf{E}_G$ of algebras Gelfand-Graev representations $G^F$; (ii) Grothendieck $\mathsf{K}_{G^\ast}$ category $G^{\ast F^\ast}$ $\overline{\mathbb{F}_q}$ (Deligne-Lusztig dual side); (ii...

The theory of frames is fundamental to timefrequency (TF or time-scale signal expansions like Gabor ysis of frames via two “TF frame representations” called the Weyl symbol and Wigner distribution of a frame. The T F analysis shows how a frame’s properties depend on the signal’s T F location and on certain frame parameters. 1 I N T R O D U C T I O N Linear time-frequency (TF) or time-scale sign...

In this paper, a new notion of frames is introduced: $ast$-operator frame as generalization of $ast$-frames in Hilbert $C^{ast}$-modules introduced by A. Alijani and M. A. Dehghan cite{Ali} and we establish some results.

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

In this paper we investigate the stability of one-sided perturbation to g-frame expansions. We show that if $Lambda$ is a g-frame of a Hilbert space $mathcal{H}$, $Lambda_{i}^{a}=Lambda_{i}+Theta_{i}$ where $Theta_{i} in mathcal{L}(mathcal{H},mathcal{H}_{i})$, and $widetilde{f}=sum_{i in J}Lambda_{i}^{star}widetilde{Lambda}_{i}^{a}f$, $widehat{f}=sum_{i in J}(Lambda_{i}^{a})^{star}widetilde{Lam...

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...