Abstract
Two-sided Clifford wavelet function (CWF) is defined in \(Cl_{(p,q)}\) with orthonormal vector basis. The properties like left linearity, right linearity, shifting, modulation dilations and power factor are established. The inversion formula for CWF is also constructed using Fourier transform. Parseval and Plancherel identities are also studied. The study is supported by certain examples related to Mathematical Physics.
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Lounesto, P.: Clifford Algebras and Spinors, 2nd edn. LMS Lecture Note Series, vol. 286, (2001)
Hitzer, E.M.: Quaternion fourier transform on quaternion fields and generalizations. Adv. Appl. Clifford Algebr. 17, 497–517 (2007). August
Hitzer, E.M.: “Tutorial on Fourier transformations and wavelet transformations in Clifford geometric algebra. Lecture Notes of the International Workshop for Computational Science with Geometric Algebra (FCSGA2007), pp. 65–87. Nagoya University, Japan (2007)
Hitzer, E.M., Mawardi, B.: Clifford fourier transform on multivector fields and uncertainty principles for dimensions \(n= 2\)(mod 4) and \(n=3\) (mod 4). Adv. Appl. Clifford Algebr. 18, 715–736 (2008). September
Pathak, R.S.: The Wavelet Transform, vol. 4. Springer Science Business Media (2009)
Chun, L.L.: A Tutorial of the wavelet Transform, p. 22. Taiwan, NTUEE (2010)
Hitzer, E.M., Abłamowicz, R.: Geometric roots of \(-1\) in clifford algebras \(Cl(p,q)\) with \(p+q\le 4\). Adv. Appl. Clifford Algebr. 21, 121–144 (2011)
Hitzer, E.M.: OPS-QFTs a new type of quaternion fourier transforms based on the orthogonal planes split with one or two general pure quaternions. AIP Conf. Proc. Am. Inst. Phys. 1, 280–283 (2011). September
Hitzer, E.M.: Clifford fourier-mellin transform with two real square roots of -1 in \(Cl (p, q), p+ q= 2\). AIP Conf. Proc. Am. Inst. Phys. 1493, 480–485 (2012). November
Hitzer, E.M., Helmstetter, J., Abłamowicz, R.: Square Roots of \(-1\) in Real Clifford Algebras in Quaternion and Clifford Fourier Transforms and Wavelets. Birkhäuser, Basel (2013). http://ar**v.org/abs/1204.4576v2
Bujack, R., Scheuermann, G., Hitzer, E.M.: A general geometric fourier transform convolution theorem. Adv. Appl. Clifford Algebr. 23, 15–38 (2013). March
Bahri, M., Ashino, R., Vaillancourt, R.: Continuous quaternion Fourier and wavelet transforms. Int. J. Wavelets Multiresolution Inf. Process. 12, (2014). https://doi.org/10.1142/S0219691314600030
Hitzer, E.M.: Two-sided clifford fourier transform with two square roots of \(-1\) in \(Cl (p, q)\). Adv. Appl. Clifford Algebr. 24, 313–332 (2014). June
Hitzer, E.M.: New Developments in Clifford Fourier Transforms. In: 2014 Advances in Applied and Pure Mathematics, Proceedings of the International Conference on Pure Mathematics, Applied Mathematics, Computational Methods (PMAMCM 2014), pp. 19–25. Santorini Island, Greece (2014)
Bromborsky, A.: An Introduction to Geometric Algebra and Calculus, (2014)
Ansari, S.J., Gorty, V.R.L.: Analysis of clifford wavelet transform in \(Cl_{(3,1)}\). Commun. (2022)
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Ansari, S.J., Lakshmi Gorty, V.R. (2023). Two-Sided Clifford Wavelet Function in Cl(p, q). In: Zeidan, D., Cortés, J.C., Burqan, A., Qazza, A., Merker, J., Gharib, G. (eds) Mathematics and Computation. IACMC 2022. Springer Proceedings in Mathematics & Statistics, vol 418. Springer, Singapore. https://doi.org/10.1007/978-981-99-0447-1_25
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