The Taylor Integral and a Generalization of the Discrete Fourier Transform
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917469628661760 |
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| author | Micheas, Athanasios Christou |
| author_facet | Micheas, Athanasios Christou |
| contents | We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the discrete Fourier transform, and we identify general conditions for it to be invertible when applied to any real or complex sequence. Applications to the mathematical sciences are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06706 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Taylor Integral and a Generalization of the Discrete Fourier Transform Micheas, Athanasios Christou General Mathematics Primary: 28A25, 65T50, Secondary: 40A05, 39A05, 94A60, 68U05 We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the discrete Fourier transform, and we identify general conditions for it to be invertible when applied to any real or complex sequence. Applications to the mathematical sciences are also presented. |
| title | The Taylor Integral and a Generalization of the Discrete Fourier Transform |
| topic | General Mathematics Primary: 28A25, 65T50, Secondary: 40A05, 39A05, 94A60, 68U05 |
| url | https://arxiv.org/abs/2605.06706 |