Darboux transformation of symmetric Jacobi matrices and Toda lattices

Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively. In this case, the Darboux transformation of J is the...

وصف كامل

التفاصيل البيبلوغرافية
الحاوية / القاعدة:Frontiers in Applied Mathematics and Statistics
المؤلفون الرئيسيون: Ivan Kovalyov, Oleksandra Levina
التنسيق: مقال
اللغة:الإنجليزية
منشور في: Frontiers Media S.A. 2024-05-01
الموضوعات:
Jacobi matrix
Darboux transformation
orthogonal polynomials
moment problem
Toda lattice
الوصول للمادة أونلاين:https://www.frontiersin.org/articles/10.3389/fams.2024.1397374/full
الوصف
الملخص:Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively. In this case, the Darboux transformation of J is the symmetric Jacobi matrix J(p) = UL (or J(d) = 𝔏𝔘), which is associated with another Toda lattice. In addition, we found explicit transformation formulas for orthogonal polynomials, m-functions and Toda lattices associated with the Jacobi matrices and their Darboux transformations.
تدمد:2297-4687

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