Factorization for the matrix-valued general Jacobi system on the full-line lattice
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908981547499520 |
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| author | Aktosun, Tuncay Choque-Rivero, Abdon E. Papanicolaou, Vassilis G. Unlu, Mehmet Weder, Ricardo |
| author_facet | Aktosun, Tuncay Choque-Rivero, Abdon E. Papanicolaou, Vassilis G. Unlu, Mehmet Weder, Ricardo |
| contents | The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the scattering from the fragments of the whole lattice by developing a factorization formula for the corresponding transition matrices. In particular, the matrix-valued transmission and reflection coefficients for the full-line lattice are explicitly expressed in terms of the scattering coefficients for the left and right lattice fragments. Since the matrix-valued scattering coefficients are easier to determine for the fragments than for the full-line lattice, the factorization formula presented provides a method to determine the scattering coefficients for full-line lattices. The theory presented is illustrated with various explicit examples, including an example demonstrating that the matrix-valued left transmission coefficient in general is not equal to the matrix-valued right transmission coefficient for a lattice. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_18229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Factorization for the matrix-valued general Jacobi system on the full-line lattice Aktosun, Tuncay Choque-Rivero, Abdon E. Papanicolaou, Vassilis G. Unlu, Mehmet Weder, Ricardo Mathematical Physics Spectral Theory 39A06, 47A40, 47B36, 81U15, 81U99 The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the scattering from the fragments of the whole lattice by developing a factorization formula for the corresponding transition matrices. In particular, the matrix-valued transmission and reflection coefficients for the full-line lattice are explicitly expressed in terms of the scattering coefficients for the left and right lattice fragments. Since the matrix-valued scattering coefficients are easier to determine for the fragments than for the full-line lattice, the factorization formula presented provides a method to determine the scattering coefficients for full-line lattices. The theory presented is illustrated with various explicit examples, including an example demonstrating that the matrix-valued left transmission coefficient in general is not equal to the matrix-valued right transmission coefficient for a lattice. |
| title | Factorization for the matrix-valued general Jacobi system on the full-line lattice |
| topic | Mathematical Physics Spectral Theory 39A06, 47A40, 47B36, 81U15, 81U99 |
| url | https://arxiv.org/abs/2511.18229 |