An SU(2n)-valued nonlinear Fourier transform
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914414144258048 |
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| author | Alexis, Michel Becker, Lars Silva, Diogo Oliveira e Thiele, Christoph |
| author_facet | Alexis, Michel Becker, Lars Silva, Diogo Oliveira e Thiele, Christoph |
| contents | We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable sequences on the half-line, and construct an inverse for $SU(2n)$-valued functions whose diagonal $n \times n$ blocks are outer matrix functions. As an application, we relate this nonlinear Fourier transform with quantum signal processing over $U(2n)$ and multivariate quantum signal processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03987 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An SU(2n)-valued nonlinear Fourier transform Alexis, Michel Becker, Lars Silva, Diogo Oliveira e Thiele, Christoph Classical Analysis and ODEs Functional Analysis Quantum Physics 42, 30 We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable sequences on the half-line, and construct an inverse for $SU(2n)$-valued functions whose diagonal $n \times n$ blocks are outer matrix functions. As an application, we relate this nonlinear Fourier transform with quantum signal processing over $U(2n)$ and multivariate quantum signal processing. |
| title | An SU(2n)-valued nonlinear Fourier transform |
| topic | Classical Analysis and ODEs Functional Analysis Quantum Physics 42, 30 |
| url | https://arxiv.org/abs/2601.03987 |