Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774540 | Journal of Mathematical Analysis and Applications | 2017 | 24 Pages |
Abstract
Let βâ¡Î²(m)={βi}iâZ+n,|i|â¤m, β0>0, denote a real n-dimensional multisequence of finite degree m. The Truncated Moment Problem concerns the existence of a positive Borel measure μ, supported in Rn, such that(0.1)βi=â«Rnxidμ(iâZ+n,|i|â¤m). We associate to βâ¡Î²(2d) an algebraic variety in Rn called the core variety, Vâ¡V(β). The core variety contains the support of each representing measure μ. We show that if V is nonempty, then β(2dâ1) has a representing measure. Moreover, if V is a nonempty compact or determining set, then β(2d) has a representing measure. We also use the core variety to exhibit a sequence β, with positive definite moment matrix and positive Riesz functional, which fails to have a representing measure.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Lawrence A. Fialkow,