References
- A. A. Arefijamaal, On construction of coherent states associated with homogeneous spaces, Turkish J. Math. 34 (2010), no. 4, 515-521.
- A. A. Arefijamaal, The continuous Zak transform and generalized Gabor frames, Mediterr. J. Math. 10 (2013), no. 1, 353-365. https://doi.org/10.1007/s00009-012-0178-4
- A. A. Arefijamaal and R. Kamyabi-Gol, On the square integrability of quasi regular representation on semidirect product groups, J. Geom. Anal. 19 (2009), no. 3, 541-552. https://doi.org/10.1007/s12220-009-9069-8
- A. A. Arefijamaal and E. Zekaee, Signal processing by alternate dual Gabor frames, Appl. Comput. Harmon. Anal. 35 (2013), no. 3, 535-540. https://doi.org/10.1016/j.acha.2013.06.001
- G. Chirikjian and A. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis With Emphasis on Rotation and Motion Groups, CRC Press. xxii, 2001.
- G. B. Folland, A Course in Abstract Harmonic Analysis, CRC press, 1995.
- A. Ghaani Farashahi, Convolution and involution on function spaces of homogeneous spaces, Bull. Malays. Math. Sci. Soc. (2) 36 (2013), no. 4, 1109-1122.
- A. Ghaani Farashahi, A unified group theoretical method for the partial Fourier analysis on semidirect product of locally compact groups, Results Math. 67 (2015), no. 1-2, 235-251. https://doi.org/10.1007/s00025-014-0407-1
- A. Ghaani Farashahi, Continuous partial Gabor transform for semi-direct product of locally compact groups, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 2, 779-803. https://doi.org/10.1007/s40840-014-0049-1
- A. Ghaani Farashahi, Abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups, J. Aust. Math. Soc. (2016), 1-17, doi:10.1017/S1446788715000798.
- A. Ghaani Farashahi, Abstract relative function *-algebras over canonical homogeneous spaces of semi-direct product groups, Southeast Asian Bull. Math. 40 (2016), no. 1, 1-13.
- A. Ghaani Farashahi, Abstract harmonic analysis of wave packet transforms over locally compact abelian groups, Banach J. Math. Anal.; http://dx.doi.org/10.1215/17358787-3721281.
- E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol 1, 1963.
- G. Hochschild, The Structure of Lie Groups, Hpolden-day, San Francisco, 1965.
- V. Kisil, Connection between two-sided and one-sided convolution type operators on non-commutative groups, Integral Equations Operator Theory 22 (1995), no. 3, 317-332. https://doi.org/10.1007/BF01378780
- V. Kisil, Relative convolutions. I. Properties and applications, Adv. Math. 147 (1999), no. 1, 35-73. https://doi.org/10.1006/aima.1999.1833
- V. Kisil, Operator covariant transform and local principle, J. Phys. A 45 (2012), no. 24, 244022, 10 pp. https://doi.org/10.1088/1751-8113/45/24/244022
-
V. Kisil, Geometry of Mobius transformations, Elliptic, parabolic and hyperbolic actions of
$SL_2({\mathbb{R}})$ , Imperial College Press, London, 2012. - V. Kisil, Erlangen program at large: an overview, Advances in applied analysis, 1-94, Trends Math., Birkhauser/Springer Basel AG, Basel, 2012.
- V. Kisil, Calculus of operators: covariant transform and relative convolutions, Banach J. Math. Anal. 8 (2014), no. 2, 156-184. https://doi.org/10.15352/bjma/1396640061
- A. Perelomov, Generalized Coherent States and Their Applications, Texts and Monographs in Physics, Springer, 1986.
- H. Reiter and J. D. Stegeman, Classical Harmonic Analysis and Locally Compact Groups, 2nd Ed, Oxford University Press, New York, 2000.
Cited by
- Abstract Coherent State Transforms Over Homogeneous Spaces of Compact Groups 2018, https://doi.org/10.1007/s11785-017-0717-x
- Abstract relative Gabor transforms over canonical homogeneous spaces of semidirect product groups with Abelian normal factor vol.15, pp.06, 2017, https://doi.org/10.1142/S0219530517500075
- Operator-Valued Continuous Gabor Transforms over Non-unimodular Locally Compact Groups vol.14, pp.3, 2017, https://doi.org/10.1007/s00009-017-0936-4
- Abstract measure algebras over homogeneous spaces of compact groups vol.29, pp.01, 2018, https://doi.org/10.1142/S0129167X18500052
- Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear PDEs vol.21, pp.1, 2019, https://doi.org/10.3390/e21010038