Darboux transformation of generalized Jacobi matrices

Kovalyov, Ivan

dc.contributor.author	Kovalyov, Ivan
dc.date.accessioned	2024-11-11T09:30:42Z
dc.date.available	2024-11-11T09:30:42Z
dc.date.issued	2014
dc.identifier.citation	Kovalyov, I. Darboux transformation of generalized Jacobi matrices / I. Kovalyov // Methods of Functional Analysis and Topology : Quarterly journal. – 2014. – Vol. 20, № 4. – pp. 301-320.	uk
dc.identifier.uri	http://enpuir.npu.edu.ua/handle/123456789/46674
dc.description.abstract	Let J be a monic generalized Jacobi matrix, i.e. a three-diagonal block matrix of special form, introduced by M. Derevyagin and V. Derkach in 2004. We find conditions for a monic generalized Jacobi matrix J to admit a factorization J = LU with L and U being lower and upper triangular two-diagonal block matrices of special form. In this case the Darboux transformation of J defined by J (p) = UL is shown to be also a monic generalized Jacobi matrix. Analogues of Christoffel formulas for polynomials of the first and the second kind, corresponding to the Darboux transformation J (p) are found.	uk
dc.language.iso	en	uk
dc.subject	Darboux transformation	uk
dc.subject	indefinite inner product	uk
dc.subject	m-function	uk
dc.subject	monic generalized Jacobi matrix	uk
dc.subject	triangular factorization	uk
dc.title	Darboux transformation of generalized Jacobi matrices	uk
dc.type	Article	uk