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PreprintCC BY 4.0arXiv

Continuity properties of the Laguerre operator and its propagator

  • Smiljana Jakšić
  • Nenad Teofanov
  • Đorđe Vučković
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Abstract

We study the well-posedness of a Cauchy problem associated with the general form of the Laguerre operator and relate it to the corresponding global problem for the harmonic oscillator. To this end, we carry out a detailed analysis of the continuity properties of the associated propagator. Furthermore, we establish connections between several integral transforms, including the fractional Fourier transform and the fractional Hankel transform. Our results highlight the role of Pilipović spaces on positive orthants when studying problems involving the Laguerre operator.

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Cite

BibTeXRIS
BibTeX
@misc{jaksic2026continuity,
  title = {{Continuity properties of the Laguerre operator and its propagator}},
  author = {Smiljana Jakšić and Nenad Teofanov and Đorđe Vučković},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.16939},
  eprint = {2605.16939},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.16939},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Continuity properties of the Laguerre operator and its propagator
AU  - Smiljana Jakšić
AU  - Nenad Teofanov
AU  - Đorđe Vučković
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2605.16939
UR  - https://arxiv.org/abs/2605.16939
AB  - We study the well-posedness of a Cauchy problem associated with the general form of the Laguerre operator and relate it to the corresponding global problem for the harmonic oscillator. To this end, we carry out a detailed analysis of the continuity properties of the associated propagator. Furthermore, we establish connections between several integral transforms, including the fractional Fourier transform and the fractional Hankel transform. Our results highlight the role of Pilipović spaces on positive orthants when studying problems involving the Laguerre operator.
ER  -