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<p>In this paper, we discuss the generalization of the Ricker wavelet transform. We also expand the Ricker wavelet transform to the generalized quotient space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathscr {B}(C^\infty ,\Delta )\)</EquationSource> </InlineEquation> and investigate its operational properties. Furthermore, we provide an illustrative example of generalized quotients that is amenable to Ricker wavelet transformation but does not fall under the category of distributions. The analysis ensures that the Ricker wavelet transform preserves structural features of generalized quotients and provides a rigorous foundation for further applications.</p>

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Ricker Wavelet Transform for Generalized Quotient Spaces

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Abhishek Singh

摘要

In this paper, we discuss the generalization of the Ricker wavelet transform. We also expand the Ricker wavelet transform to the generalized quotient space \(\mathscr {B}(C^\infty ,\Delta )\) and investigate its operational properties. Furthermore, we provide an illustrative example of generalized quotients that is amenable to Ricker wavelet transformation but does not fall under the category of distributions. The analysis ensures that the Ricker wavelet transform preserves structural features of generalized quotients and provides a rigorous foundation for further applications.