Fourier transforms of orthogonal structures on the paraboloid
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918136340545536 |
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| author | Çetin, Hasan Özkan Karaman, Rabia Aktaş |
| author_facet | Çetin, Hasan Özkan Karaman, Rabia Aktaş |
| contents | The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal structures on the paraboloid such as Laguerre polynomials on the paraboloid and Jacobi polynomials on the paraboloid, and to define two new families of multivariate orthogonal functions by using Parseval's identity. In addition, some contiguous relations for these families of functions are given, and the obtained results are expressed in terms of the continuous Hahn polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier transforms of orthogonal structures on the paraboloid Çetin, Hasan Özkan Karaman, Rabia Aktaş Classical Analysis and ODEs 33C50, 33C70, 33C45 The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal structures on the paraboloid such as Laguerre polynomials on the paraboloid and Jacobi polynomials on the paraboloid, and to define two new families of multivariate orthogonal functions by using Parseval's identity. In addition, some contiguous relations for these families of functions are given, and the obtained results are expressed in terms of the continuous Hahn polynomials. |
| title | Fourier transforms of orthogonal structures on the paraboloid |
| topic | Classical Analysis and ODEs 33C50, 33C70, 33C45 |
| url | https://arxiv.org/abs/2509.04994 |