Abstract

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.
Original languageEnglish
Title of host publicationМарчуковские научные чтения - 2019
Subtitle of host publicationТруды Международной конференции "Актуальные проблемы вычислительной и прикладной математики"
Place of PublicationНовосибирск
PublisherИздательство Новосибирского университета
Pages339-345
ISBN (Print)9785901548424
DOIs
Publication statusPublished - 16 Dec 2019
EventМеждународная конференция "Актуальные проблемы вычислительной и прикладной математики 2019" - Новосибирск
Duration: 1 Jul 20195 Jul 2019

Conference

ConferenceМеждународная конференция "Актуальные проблемы вычислительной и прикладной математики 2019"
Abbreviated titleАПВПМ - 19
CountryRussian Federation
CityНовосибирск
Period1/07/195/07/19

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