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Existence of representation frames based on wave packet groups

Ali Akbar AREFİJAMAAL [1] , Atefe Razghandi [2]

Let $H$ be a locally compact group, $K$ a locally compact abelian group with dual group $\hat{K}$. In this article, we consider the wave packet group $G_{\Theta}$ which is the semidirect product of locally compact groups $H$ and $K\times \hat{K}$, where $\Theta$ is a continuous homomorphism from $H$ into $Aut(K\times\hat{K})$. We review the quasi regular representation on $G_{\Theta}$ and extend the continuous Zak transform to $L^{2}(G_{\Theta})$. Moreover, we state a continuous frame based on $G_{\Theta}$ to reconstruct the element of $L^{2}\left(K\times \hat{K}\right)$. These results are extended to more general wave packet groups. Finally, we establish some methods to find dual of such continuous frames in the form of original frames.
semidirect product groups, quasi regular representation, wave packet groups
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Primary Language en Mathematics Mathematics Orcid: 0000-0003-2153-352XAuthor: Ali Akbar AREFİJAMAAL (Primary Author)Institution: Hakim Sabzevari UniversityCountry: Iran Orcid: 0000-0002-5253-1730Author: Atefe Razghandi Institution: Hakim Sabzevari UniversityCountry: Iran Publication Date : October 6, 2020
 Bibtex @research article { hujms540946, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1825 - 1842}, doi = {10.15672/hujms.540946}, title = {Existence of representation frames based on wave packet groups}, key = {cite}, author = {Arefi̇jamaal, Ali Akbar and Razghandi, Atefe} } APA Arefi̇jamaal, A , Razghandi, A . (2020). Existence of representation frames based on wave packet groups . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1825-1842 . DOI: 10.15672/hujms.540946 MLA Arefi̇jamaal, A , Razghandi, A . "Existence of representation frames based on wave packet groups" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1825-1842 Chicago Arefi̇jamaal, A , Razghandi, A . "Existence of representation frames based on wave packet groups". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1825-1842 RIS TY - JOUR T1 - Existence of representation frames based on wave packet groups AU - Ali Akbar Arefi̇jamaal , Atefe Razghandi Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.540946 DO - 10.15672/hujms.540946 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1825 EP - 1842 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.540946 UR - https://doi.org/10.15672/hujms.540946 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Existence of representation frames based on wave packet groups %A Ali Akbar Arefi̇jamaal , Atefe Razghandi %T Existence of representation frames based on wave packet groups %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.540946 %U 10.15672/hujms.540946 ISNAD Arefi̇jamaal, Ali Akbar , Razghandi, Atefe . "Existence of representation frames based on wave packet groups". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1825-1842 . https://doi.org/10.15672/hujms.540946 AMA Arefi̇jamaal A , Razghandi A . Existence of representation frames based on wave packet groups. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1825-1842. Vancouver Arefi̇jamaal A , Razghandi A . Existence of representation frames based on wave packet groups. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1825-1842.

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