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The Problem of Moments. New York: American mathematical society. ISBN 978-1-4704-1228-9. Akhiezer, Naum I. (1965). The classical moment problem and some related questions in analysis. New York: Hafner Publishing Co. (translated from the Russian by N. Kemmer) Kreĭn, M. G.; Nudel′man, A. A. (1977). The Markov Moment Problem and Extremal ...
So in this case the solution to the Hamburger moment problem is unique and μ, being the spectral measure of T, has finite support. More generally, the solution is unique if there are constants C and D such that, for all n, | m n | ≤ CD n n! (Reed & Simon 1975, p. 205). This follows from the more general Carleman's condition.
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions (indeterminate moment problem) whereas a Hausdorff moment problem always has a unique solution if it is solvable (determinate moment problem). In the indeterminate moment problem case, there are infinite measures ...
The essential difference between this and other well-known moment problems is that this is on a half-line [0, ∞), whereas in the Hausdorff moment problem one considers a bounded interval [0, 1], and in the Hamburger moment problem one considers the whole line (−∞, ∞).
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.
The Classical Moment Problem and Some Related Questions in Analysis. Philadelphia, PA: Society for Industrial and Applied Mathematics. doi: 10.1137/1.9781611976397. ISBN 978-1-61197-638-0. Akhiezer, N.I.; Kreĭn, M.G. (1962). Some Questions in the Theory of Moments. Translations of mathematical monographs. American Mathematical Society.
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In mathematics, particularly, in analysis, Carleman's condition gives a sufficient condition for the determinacy of the moment problem. That is, if a measure μ {\displaystyle \mu } satisfies Carleman's condition, there is no other measure ν {\displaystyle \nu } having the same moments as μ . {\displaystyle \mu .}