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<p>In this study, fundamental properties of a class of finite Mellin transformations in a recurrent set of generalized functions are investigated. An appropriate set of delta sequences, two sets of <i>c</i>-recurrent Boehmians, and certain convolution theorems are identified. The proposed sets of recurrent Boehmians are allocated, generalizing the standard sets of classical functions. The new generalized Mellin operator is then extended to the recurrent sets of Boehmians and shown to be linear, onto, and one-to-one mapping. Additionally, with regard to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation>- and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Delta \)</EquationSource> </InlineEquation>-convergences, the transform in question is continuous. An inversion formula and several properties are also provided.</p>

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Certain results associated with a finite integral transform and its generalization to recurrent Boehmian spaces

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Shrideh Al-Omari

摘要

In this study, fundamental properties of a class of finite Mellin transformations in a recurrent set of generalized functions are investigated. An appropriate set of delta sequences, two sets of c-recurrent Boehmians, and certain convolution theorems are identified. The proposed sets of recurrent Boehmians are allocated, generalizing the standard sets of classical functions. The new generalized Mellin operator is then extended to the recurrent sets of Boehmians and shown to be linear, onto, and one-to-one mapping. Additionally, with regard to \(\delta \) - and \(\Delta \) -convergences, the transform in question is continuous. An inversion formula and several properties are also provided.