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Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space

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Abstract

By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general setting of Gaussian processes. Our results serve to unify existing tools from infinite-dimensional analysis.

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Acknowledgements

The co-authors thank the following colleagues for helpful and enlightening discussions: Professors Daniel Alpay, Sergii Bezuglyi, Ilwoo Cho, Wayne Polyzou, David Stewart, Eric S. Weber, and members in the Math Physics seminar at The University of Iowa.

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Authors and Affiliations

  1. Department of Mathematics, The University of Iowa, Iowa City, IA, 52242-1419, USA

    Palle E. T. Jorgensen

  2. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, 62026, USA

    Myung-Sin Song

  3. Mathematical Reviews, 416 4th Street, Ann Arbor, MI, 48103-4816, USA

    James Tian

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  1. Palle E. T. Jorgensen
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Correspondence to Myung-Sin Song.

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The authors did not receive support from any organization for the submitted work. The authors have no relevant financial or non-financial interests to disclose. Palle Jorgensen, Myung-Sin Song, James Tian.

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Communicated by Laura De Carli.

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Jorgensen, P.E.T., Song, MS. & Tian, J. Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space. Sampl. Theory Signal Process. Data Anal. 21, 12 (2023). https://doi.org/10.1007/s43670-023-00051-z

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