The Classical Moment Problem and Generalized Indefinite Strings

We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. More precisely, we introduce the class of Krein–Langer strings and show that there is a bijective correspondence between moment sequences and this class of generalized indefinite strings. This result can be viewed as a complement to the classical results of Krein on the connection between the Stieltjes moment problem and Krein–Stieltjes strings and Kac on the connection between the Hamburger moment problem and 2 × 2 canonical systems with Hamburger Hamiltonians. © 2018, The Author(s).

Авторы
Eckhardt J.1 , Kostenko A. 1, 2, 3
Издательство
Springer Basel
Номер выпуска
2
Язык
Английский
Статус
Опубликовано
Номер
23
Том
90
Год
2018
Организации
  • 1 Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, 1090, Austria
  • 2 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ul. 19, Ljubljana, 1000, Slovenia
  • 3 RUDN University, Miklukho-Maklaya Str. 6, Moscow, 117198, Russian Federation
Ключевые слова
Generalized indefinite strings; Hamburger moment problem
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6750/