Calderon's reproducing formula and extremal functions associated with the linear canonical Dunkl wavelet transform
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912373462269952 |
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| author | Verma, Sandeep Kumar S, Umamaheswari |
| author_facet | Verma, Sandeep Kumar S, Umamaheswari |
| contents | In this article, we undertake a two-fold investigation. First, we establish Calderons reproducing formula for the linear canonical Dunkl continuous wavelet transform. Further, we define the reproducing kernel linear canonical Dunkl Sobolev space and introduce a novel inner product associated with the continuous wavelet transform in this space. We then derive explicit formulas for the reproducing kernels and present several related results. In the second part, we investigate extremal functions associated with both the continuous wavelet and linear canonical Dunkl transform. In particular, we characterize the extremal functions, represent them in terms of the corresponding reproducing kernels, and establish structural properties relevant to their formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calderon's reproducing formula and extremal functions associated with the linear canonical Dunkl wavelet transform Verma, Sandeep Kumar S, Umamaheswari Functional Analysis 42C40, 51F15, 44A20, 43A32, 46E22, 44A35 In this article, we undertake a two-fold investigation. First, we establish Calderons reproducing formula for the linear canonical Dunkl continuous wavelet transform. Further, we define the reproducing kernel linear canonical Dunkl Sobolev space and introduce a novel inner product associated with the continuous wavelet transform in this space. We then derive explicit formulas for the reproducing kernels and present several related results. In the second part, we investigate extremal functions associated with both the continuous wavelet and linear canonical Dunkl transform. In particular, we characterize the extremal functions, represent them in terms of the corresponding reproducing kernels, and establish structural properties relevant to their formulation. |
| title | Calderon's reproducing formula and extremal functions associated with the linear canonical Dunkl wavelet transform |
| topic | Functional Analysis 42C40, 51F15, 44A20, 43A32, 46E22, 44A35 |
| url | https://arxiv.org/abs/2505.08440 |