Moment Problems & Discrete Approximation

← Back to Domain-Specific Families

Abstractions about moment sequences and matrices, classical moment problems, secondary measures, and finite-difference coefficients.

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Finite Difference Coefficient — A stencil weight determined by derivative order, evaluation point, sample-node offsets, and polynomial exactness so their weighted samples approximate the target derivative with a declared truncation order.
• Hamburger moment problem — The problem of deciding whether a given sequence is the sequence of moments of a positive Borel measure on the whole real line, and whether that representing measure is unique.
• Hausdorff moment problem — The problem of characterizing sequences that are moments of a positive measure on the unit interval, with a unique representing measure whenever one exists.
• Moment matrix — A symmetric matrix indexed by monomials whose entry at two indices is the moment associated with their product, encoding a moment sequence and positivity constraints.
• Moment problem — The inverse problem of deciding whether a sequence is represented by moments of a measure, and whether that representing measure is unique.
• Secondary Measure — An auxiliary positive measure derived from an initial moment measure so that its secondary-polynomial sequence becomes orthogonal, with the pair linked by a reciprocal Stieltjes-transform relation.
• Stieltjes moment problem — The problem of deciding whether a sequence is the moment sequence of a positive measure on the nonnegative half-line and whether that measure is unique.