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On Modified Mellin Transform of Generalized Functions

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  • S. K. Q. Al-Omari
  • Adem Kılıçman

Abstract

We investigate the modified Mellin transform on certain function space of generalized functions. We first obtain the convolution theorem for the classical and distributional modified Mellin transform. Then we describe the domain and range spaces where the extended modified transform is well defined. Consistency, convolution, analyticity, continuity, and sufficient theorems for the proposed transform have been established. An inversion formula is also obtained and many properties are given.

Suggested Citation

  • S. K. Q. Al-Omari & Adem Kılıçman, 2013. "On Modified Mellin Transform of Generalized Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, December.
    • Handle: RePEc:hin:jnlaaa:539240
    DOI: 10.1155/2013/539240
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