On Some q-Bessel Type Continuous Wavelet Transform
Boletim da Sociedade Paranaense de Matematica, ISSN: 2175-1188, Vol: 42, Page: 1-19
2024
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Article Description
In this paper we continue to exploit the modified variants of Bessel function in the framework of q-theory to construct wavelet operators. A generalized q-Bessel type function is introduced leading to an associated mother wavelet which in turns induced a continuous wavelet transform. Finally, Plancherel/Parceval type relations are proved. Such variant of wavelets permits to approximate solutions of PDEs by transforming them to recurrent sequences. Numerical examples are provided with graphical illustrations and error estimates to confirm these theoretical findings.
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