Wavelet-based inversion and analysis of Flett, Riesz and bi-parametric potentials in $(k,1)$ generalized Fourier framework
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908489906913280 |
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| author | P, Athulya S, Umamaheswari Verma, Sandeep Kumar |
| author_facet | P, Athulya S, Umamaheswari Verma, Sandeep Kumar |
| contents | In this paper, we construct and analyze Bessel and Flett potentials associated with the heat and Poisson semigroups in the framework of the $(k,1)$-generalized Fourier transform. We establish fundamental properties of these potentials and derive an explicit inversion formula for the Flett potential using a wavelet-like transform. Furthermore, we introduce a $β$-semigroup $\mathcal{B}_k^{(β,t)}$, defined via $W_k^{(β, t)}$, which enables the formulation of an inversion formula for the Riesz potential. As a unifying extension, we define and investigate bi-parametric potentials $\mathfrak{J}_k^{(α,β)}$, which generalize both the Bessel potential and the Flett potential. In addition, we define the associated function spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wavelet-based inversion and analysis of Flett, Riesz and bi-parametric potentials in $(k,1)$ generalized Fourier framework P, Athulya S, Umamaheswari Verma, Sandeep Kumar Functional Analysis In this paper, we construct and analyze Bessel and Flett potentials associated with the heat and Poisson semigroups in the framework of the $(k,1)$-generalized Fourier transform. We establish fundamental properties of these potentials and derive an explicit inversion formula for the Flett potential using a wavelet-like transform. Furthermore, we introduce a $β$-semigroup $\mathcal{B}_k^{(β,t)}$, defined via $W_k^{(β, t)}$, which enables the formulation of an inversion formula for the Riesz potential. As a unifying extension, we define and investigate bi-parametric potentials $\mathfrak{J}_k^{(α,β)}$, which generalize both the Bessel potential and the Flett potential. In addition, we define the associated function spaces. |
| title | Wavelet-based inversion and analysis of Flett, Riesz and bi-parametric potentials in $(k,1)$ generalized Fourier framework |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2508.10406 |