Document Type: Research Paper

Authors

Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran.

Abstract

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to a uniform lattice of $G$.

Keywords

Main Subjects

[1] G.B. Folland, A Course in Abstract Harmonic Analysis, CRC Press., London, 1995.

[2] H. Fuhr, Abstract Harmonic Analysis of Continuous Wavelet Transforms, Springer-Verlag, Berlin, 2005.

[3] A. Grossmann, J. Morlet, and T. Paul, Transforms associated to square integrable group representations I, J. Math. Phys., 26 (1985), pp. 2473-2479.

[4] P.E.T. Jorgensen, K.D. Merrill and J.A. Packer, Representations, Wavelets and Frames, Applied and Numerical Harmonic Analysis, Birkhäuser, 2008.

[5] A. Khosravi and B. Khosravi, Frames and bases in tensor products of Hilbert spaces and Hilbert $C^*$-modules, Proc. Indian Acad. Sci., 117 (2003), pp. 1-12.

[6] B.H. Sadathoseyni and S.M. Tabatabaie, Coorbit spaces related to locally compact hypergroups, Acta Math. Hungar., 153 (2017), pp. 177-196.

[7] S.M. Tabatabaie and S. Jokar, A characterization of admissible vectors related to representations on hypergroups, Tbil. Math. J., 10 (2017), pp. 143-151.

[8] D.P. Williams, Crossed Products of $C^*$-Algebras, Mathematical surveys and monographs, 2007.