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Cauchy-type determi...
Abstract
Ämnesord
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- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Cauchy-type determinants; Integrable systems; Multiple-pole solutions; Sylvester equation
- MATHEMATICS
- MATEMATIK
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