Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
DYNAMIC APPROACH TO CLASSICAL MOMENT PROBLEM. / Mikhaylov, A.S.; Mikahaylov, V.S.
Марчуковские научные чтения - 2019: Труды Международной конференции "Актуальные проблемы вычислительной и прикладной математики". Новосибирск : Издательство Новосибирского университета, 2019. стр. 339-345.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - DYNAMIC APPROACH TO CLASSICAL MOMENT PROBLEM
AU - Mikhaylov, A.S.
AU - Mikahaylov, V.S.
PY - 2019/12/16
Y1 - 2019/12/16
N2 - We consider the problem of the construction of a measure supported on a real line from prescribed moments. The main idea is to use the auxiliary dynamical system with the discrete time associated with a semi-infinite Jacobi matrix. Then the inverse dynamic data for this system, so called response operator (discrete analog of a dynamic Dirichet-to-Neumann map) is given in terms of moments, and we can use ideas of the Boundary Control method to recover the spectral data, i.e. the measure of a truncated moments problem, from dynamic one. The remarkable fact is that in our procedure we do not use the Jacobi matrix itself. We also formulate the results on the uniqueness of the solution of Hamburger and Stieltjes moments problems.
AB - We consider the problem of the construction of a measure supported on a real line from prescribed moments. The main idea is to use the auxiliary dynamical system with the discrete time associated with a semi-infinite Jacobi matrix. Then the inverse dynamic data for this system, so called response operator (discrete analog of a dynamic Dirichet-to-Neumann map) is given in terms of moments, and we can use ideas of the Boundary Control method to recover the spectral data, i.e. the measure of a truncated moments problem, from dynamic one. The remarkable fact is that in our procedure we do not use the Jacobi matrix itself. We also formulate the results on the uniqueness of the solution of Hamburger and Stieltjes moments problems.
KW - moment problem
KW - boundary control method
KW - Jacobi Matrices
UR - http://conf.nsc.ru/files/conferences/amca2019/554130/%D0%90%D0%9F%D0%92%D0%9F%D0%9C-2019.pdf
U2 - 10.24411/9999-016A-2019-10054
DO - 10.24411/9999-016A-2019-10054
M3 - Conference contribution
SN - 9785901548424
SP - 339
EP - 345
BT - Марчуковские научные чтения - 2019
PB - Издательство Новосибирского университета
CY - Новосибирск
T2 - Международная конференция "Актуальные проблемы вычислительной и прикладной математики 2019"
Y2 - 1 July 2019 through 5 July 2019
ER -
ID: 49668124