Abstract
The two-sided Hamburger moment problem1, also called the strong one [4], has been extensively studied in recent years in connection with rational approximation. We propose to consider the question of when a sequence, say {a n } ∞ n=0 can be extended backwards so that the resulting sequence {a n } ∞ n=−N has an integral representation of the Hamburger type. This was settled (without any proof) under different circumstances in [6]. Here we wish to discuss this completely, as well as the possibility of extending {a n } ∞ n=0 to {a n } ∞ n−∞ .
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Szafraniec, F.H. On extending backwards positive definite sequences. Numer Algor 3, 419–425 (1992). https://doi.org/10.1007/BF02141949
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DOI: https://doi.org/10.1007/BF02141949