Inverse spectral problem for Jacobi operators and Miura transformation

We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the m...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Osipov Andrey
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	jacobi operators positive operators deficiency indices power moment problem toda lattices volterra lattices miura transformations 44a60 47b36 37k10 37k15 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/eee9ccec0f7a42bd999991750ce717c8
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:eee9ccec0f7a42bd999991750ce717c8
record_format	dspace
spelling	oai:doaj.org-article:eee9ccec0f7a42bd999991750ce717c82021-12-05T14:10:45ZInverse spectral problem for Jacobi operators and Miura transformation2299-328210.1515/conop-2020-0116https://doaj.org/article/eee9ccec0f7a42bd999991750ce717c82021-06-01T00:00:00Zhttps://doi.org/10.1515/conop-2020-0116https://doaj.org/toc/2299-3282We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the moments of its Weyl function, can be used in solving initial-boundary value problem for both systems. It is shown that the Miura transformation can be easily described in terms of these moments. Using this description we establish a bijection between the Volterra lattices and the class of Toda lattices which is characterized by positivity of Jacobi operators in their Lax representation. Also, we discuss an implication of the latter result to the spectral theory.Osipov AndreyDe Gruyterarticlejacobi operatorspositive operatorsdeficiency indicespower moment problemtoda latticesvolterra latticesmiura transformations44a6047b3637k1037k15MathematicsQA1-939ENConcrete Operators, Vol 8, Iss 1, Pp 77-89 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	jacobi operators positive operators deficiency indices power moment problem toda lattices volterra lattices miura transformations 44a60 47b36 37k10 37k15 Mathematics QA1-939
spellingShingle	jacobi operators positive operators deficiency indices power moment problem toda lattices volterra lattices miura transformations 44a60 47b36 37k10 37k15 Mathematics QA1-939 Osipov Andrey Inverse spectral problem for Jacobi operators and Miura transformation
description	We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the moments of its Weyl function, can be used in solving initial-boundary value problem for both systems. It is shown that the Miura transformation can be easily described in terms of these moments. Using this description we establish a bijection between the Volterra lattices and the class of Toda lattices which is characterized by positivity of Jacobi operators in their Lax representation. Also, we discuss an implication of the latter result to the spectral theory.
format	article
author	Osipov Andrey
author_facet	Osipov Andrey
author_sort	Osipov Andrey
title	Inverse spectral problem for Jacobi operators and Miura transformation
title_short	Inverse spectral problem for Jacobi operators and Miura transformation
title_full	Inverse spectral problem for Jacobi operators and Miura transformation
title_fullStr	Inverse spectral problem for Jacobi operators and Miura transformation
title_full_unstemmed	Inverse spectral problem for Jacobi operators and Miura transformation
title_sort	inverse spectral problem for jacobi operators and miura transformation
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/eee9ccec0f7a42bd999991750ce717c8
work_keys_str_mv	AT osipovandrey inversespectralproblemforjacobioperatorsandmiuratransformation
_version_	1718371772408004608

Inverse spectral problem for Jacobi operators and Miura transformation

Ejemplares similares