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Stieltjes moment problem, the Glossary

In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1, m2,...) to be of the form for some measure μ.^[1]

Carleman's condition

In mathematics, particularly, in analysis, Carleman's condition gives a sufficient condition for the determinacy of the moment problem. Stieltjes moment problem and Carleman's condition are Mathematical analysis and moment (mathematics).

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Hamburger moment problem

In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2,...), does there exist a positive Borel measure μ (for instance, the measure determined by the cumulative distribution function of a random variable) on the real line such that In other words, an affirmative answer to the problem means that (m0, m1, m2,...) is the sequence of moments of some positive Borel measure μ. Stieltjes moment problem and Hamburger moment problem are Mathematical problems, moment (mathematics) and probability problems.

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Hankel matrix

In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant.

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Hausdorff moment problem

In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence be the sequence of moments of some Borel measure supported on the closed unit interval. Stieltjes moment problem and Hausdorff moment problem are Mathematical problems, moment (mathematics) and probability problems.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Measure (mathematics)

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.

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Moment problem

In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure \mu to the sequence of moments More generally, one may consider for an arbitrary sequence of functions M_n. Stieltjes moment problem and moment problem are Mathematical analysis, Mathematical problems, moment (mathematics) and probability problems.

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