Inverses of integral transforms of RKHSs
Functional Analysis
2024-12-30 v1 Complex Variables
Abstract
The Fourier transform and its inverse are well-known to have complex conjugate integral kernels. S.~Saitoh demonstrated that this relationship extends to the theory of integral transforms of Hilbert spaces of functions under certain conditions. In this paper, we derive a necessary and sufficient condition for the inverse of an integral transform of a Hilbert space of functions to be represented by a complex conjugate integral kernel. As an application, we present an alternative proof of Plancherel's theorem using the theory of reproducing kernels.
Cite
@article{arxiv.2412.19047,
title = {Inverses of integral transforms of RKHSs},
author = {Akira Yamada},
journal= {arXiv preprint arXiv:2412.19047},
year = {2024}
}