Probability problems | Moment (mathematics) | Functional analysis | Measure theory | Mathematical problems

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. The Stieltjes moment problem, , and the Hausdorff moment problem are similar but replace the real line by (Stieltjes and Vorobyev; but Vorobyev formulates the problem in the terms of matrix theory), or a bounded interval (Hausdorff). (Wikipedia).

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Related pages

Borel measure | Moment (mathematics) | Self-adjoint operator | Carleman's condition | Cumulative distribution function | Symmetric operator | Kronecker delta | Polynomial | Sequence | Laplace transform | Extensions of symmetric operators | Multiplication operator | Equivalence class | Mathematics | Integer | Moment problem | Hankel matrix | Random variable | Shift operator | Hilbert space | Hausdorff moment problem | Complex number | Orthogonal polynomials | Stieltjes moment problem | Cayley transform