Fourier representations of fractional B Splines via generalized Stirling type polynomials
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913130494296064 |
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| author | Gun, Damla Massopust, Peter Simsek, Yilmaz |
| author_facet | Gun, Damla Massopust, Peter Simsek, Yilmaz |
| contents | In this paper, we investigate fractional B splines and their connections with Fourier analysis, and establish connections with generalized Stirling-type numbers and distribution theory. Employing a generating function approach inspired by recent results of Simsek [24], we derive a novel Fourier type expansion for fractional B splines that involves generalized Stirling type numbers. Our main contribution is the derivation of a Fourier-type expansion of fractional B splines in terms of generalized Stirling-type numbers. This representation allows us to express fractional B splines as infinite linear combinations of derivatives of the Dirac delta in the distributional sense. Furthermore, we establish an explicit shifted distributional representation and obtain shifted distributional representations that characterize the action of fractional B-splines on test functions. In addition, we introduce a new class of fractional spline polynomials and derive their generating function in terms of the Mittag Leffler function. These results provide a unified framework that connects spline theory, fractional calculus, and combinatorial structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15244 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fourier representations of fractional B Splines via generalized Stirling type polynomials Gun, Damla Massopust, Peter Simsek, Yilmaz General Mathematics 05A15, 11B68, 11B73, 12D10, 26A33, 41A15, 46F12 In this paper, we investigate fractional B splines and their connections with Fourier analysis, and establish connections with generalized Stirling-type numbers and distribution theory. Employing a generating function approach inspired by recent results of Simsek [24], we derive a novel Fourier type expansion for fractional B splines that involves generalized Stirling type numbers. Our main contribution is the derivation of a Fourier-type expansion of fractional B splines in terms of generalized Stirling-type numbers. This representation allows us to express fractional B splines as infinite linear combinations of derivatives of the Dirac delta in the distributional sense. Furthermore, we establish an explicit shifted distributional representation and obtain shifted distributional representations that characterize the action of fractional B-splines on test functions. In addition, we introduce a new class of fractional spline polynomials and derive their generating function in terms of the Mittag Leffler function. These results provide a unified framework that connects spline theory, fractional calculus, and combinatorial structures. |
| title | Fourier representations of fractional B Splines via generalized Stirling type polynomials |
| topic | General Mathematics 05A15, 11B68, 11B73, 12D10, 26A33, 41A15, 46F12 |
| url | https://arxiv.org/abs/2605.15244 |