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The Weinstein transform theory is utilized in this study to define the space \(H(A)\) and demonstrates that the Weinstein transform \(\mathcal {F}_{w}(\phi )\) is an automorphism on the space \(H(A)\) . The Banach space-valued test functions of Beurling type ultradistribution \(H_{\omega }(A)\) is explained by adopting the weight function \(\omega \) . The subspace \(D_{\mathbb {R}^{n+1}_{+}}(A)\) is shown to be dense in \( H_{\omega }(A)\) and the Weinstein transform \(\mathcal {F}_{w}(\phi )\) is an automorphism on the space \( H_{\omega }(A)\) . Furthermore, it is also shown in the paper that the linear space ) is dense in \(H_{\omega }(A)\) .

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Banach-Space-Valued Ultradistributions Involving the Weinstein Transform

  • 会议论文

  • 发表日期：

    2025年

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  • Sitaram Yadav,
  • Santosh Kumar Upadhyay

摘要

The Weinstein transform theory is utilized in this study to define the space \(H(A)\) and demonstrates that the Weinstein transform \(\mathcal {F}_{w}(\phi )\) is an automorphism on the space \(H(A)\) . The Banach space-valued test functions of Beurling type ultradistribution \(H_{\omega }(A)\) is explained by adopting the weight function \(\omega \) . The subspace \(D_{\mathbb {R}^{n+1}_{+}}(A)\) is shown to be dense in \( H_{\omega }(A)\) and the Weinstein transform \(\mathcal {F}_{w}(\phi )\) is an automorphism on the space \( H_{\omega }(A)\) . Furthermore, it is also shown in the paper that the linear space ) is dense in \(H_{\omega }(A)\) .