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PreprintCC BY 4.0arXiv

Characterization of Integral Transforms for Hilbert Space-Valued Functions

  • Satyajyoti Achar
  • Ramesh Manna
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Abstract

The aim of this paper is to characterize the Fourier transform of functions taking values in a separable Hilbert space Hi and defined on locally compact abelian groups. Inspired by Krukowskis characterization of integral transforms on locally compact abelian groups, we establish characterizations of the Fourier, Laplace, and cosine transforms for separable Hilbert space-valued functions on locally compact abelian groups. Furthermore, we obtain a characterization of the group Fourier transform on the Heisenberg group.

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Cite

BibTeXRIS
BibTeX
@misc{achar2026characterization,
  title = {{Characterization of Integral Transforms for Hilbert Space-Valued Functions}},
  author = {Satyajyoti Achar and Ramesh Manna},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04698},
  eprint = {2611.04698},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04698},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Characterization of Integral Transforms for Hilbert Space-Valued Functions
AU  - Satyajyoti Achar
AU  - Ramesh Manna
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04698
UR  - https://arxiv.org/abs/2611.04698
AB  - The aim of this paper is to characterize the Fourier transform of functions taking values in a separable Hilbert space Hi and defined on locally compact abelian groups. Inspired by Krukowskis characterization of integral transforms on locally compact abelian groups, we establish characterizations of the Fourier, Laplace, and cosine transforms for separable Hilbert space-valued functions on locally compact abelian groups. Furthermore, we obtain a characterization of the group Fourier transform on the Heisenberg group.
ER  -