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- W2053109991 abstract "It is well known that the Sylvester matrix equation AX + XB = C has a unique solution X if and only if 0 ∉ spec(A) + spec(B). The main result of the present article are explicit formulas for the determinant of X in the case that C is one-dimensional. For diagonal matrices A, B, we reobtain a classical result by Cauchy as a special case. The formulas we obtain are a cornerstone in the asymptotic classification of multiple pole solutions to integrable systems like the sine-Gordon equation and the Toda lattice. We will provide a concise introduction to the background from soliton theory, an operator theoretic approach originating from work of Marchenko and Carl, and discuss examples for the application of the main results." @default.
- W2053109991 created "2016-06-24" @default.
- W2053109991 creator A5018101412 @default.
- W2053109991 date "2010-08-01" @default.
- W2053109991 modified "2023-09-27" @default.
- W2053109991 title "Cauchy-type determinants and integrable systems" @default.
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- W2053109991 doi "https://doi.org/10.1016/j.laa.2010.03.011" @default.
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