Continuity properties of the Laguerre operator and its propagator
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909049868517376 |
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| author | Jakšić, Smiljana Teofanov, Nenad Vučković, Đorđe |
| author_facet | Jakšić, Smiljana Teofanov, Nenad Vučković, Đorđe |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16939 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuity properties of the Laguerre operator and its propagator Jakšić, Smiljana Teofanov, Nenad Vučković, Đorđe Analysis of PDEs Functional Analysis 46F05, 33C45 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. |
| title | Continuity properties of the Laguerre operator and its propagator |
| topic | Analysis of PDEs Functional Analysis 46F05, 33C45 |
| url | https://arxiv.org/abs/2605.16939 |