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On a criterion for the determinate-indeterminate dichotomy of the moment problem
- Publication Year :
- 2021
-
Abstract
- When the classical Hamburger moment problem has solutions, it has either exactly one solution or infinitely many solutions. Correspondingly, the moment problem is said to be either determinate or indeterminate. In terms of Jacobi operators, this dichotomy translates into the operator being either selfadjoint or symmetric nonselfadjoint. In this work, we present a new criterion for the determinate-indeterminate classification which hinges on bases of representation (in Akhiezer-Glazman terminology) for Jacobi operators so that the corresponding matrices have a certain structure.<br />Comment: 23 pages. A new section was added and some minor changes were made along the text. Corrections in references and citations
- Subjects :
- Mathematical Physics
Mathematics - Spectral Theory
47B32, 47B36, 30E05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2107.00697
- Document Type :
- Working Paper