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<p>In this paper, we define an integral transform of cylinder functionals on abstract Wiener space with respect to a given orthonormal set in the Hilbert space <i>H</i>. We establish an existence theorem for this integral transform and address related topics. Additionally, we investigate the impact of changing the orthonormal set on the kernel of the integral transform through the composition formula, the convolution theorem, and the Cameron-Storvick type theorem.</p>

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Some Effects of Changing the Orthonormal Set for an Integral Transform

  • 期刊论文

  • 发表日期：

    2025年2月27日

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  • Hyun Soo Chung

摘要

In this paper, we define an integral transform of cylinder functionals on abstract Wiener space with respect to a given orthonormal set in the Hilbert space H. We establish an existence theorem for this integral transform and address related topics. Additionally, we investigate the impact of changing the orthonormal set on the kernel of the integral transform through the composition formula, the convolution theorem, and the Cameron-Storvick type theorem.