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Continued Fractions and Strong Hamburger Moment Problems
Author(s) -
Jones William B.,
Njåstad Olav,
Thron W. J.
Publication year - 1983
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-47.2.363
Subject(s) - mathematics , uniqueness , moment (physics) , convergence (economics) , sequence (biology) , fraction (chemistry) , mathematical analysis , pure mathematics , combinatorics , classical mechanics , physics , organic chemistry , biology , genetics , chemistry , economics , economic growth
APT‐fractions are introduced. They include the positive T ‐fractions as a special case. APT‐fractions have integral representations of the form∫ ‐ ∞ ∞d ψ ( t )z + tSufficient conditions for ordinary convergence are derived and complete convergence is introduced and shown to be independent of the parameter z . This is important for solving the uniqueness question for the strong Hamburger moment problem in those cases for which the sequence{ c n }‐ ∞ ∞has a corresponding APT‐fraction.
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