Loading...
Please wait, while we are loading the content...
Similar Documents
Solution of the Truncated Hyperbolic Moment Problem
| Content Provider | Semantic Scholar |
|---|---|
| Author | Curto, Raul Fialkow, Lawrence A. |
| Copyright Year | 2004 |
| Abstract | Let Q(x, y) = 0 be an hyperbola in the plane. Given real numbers β ≡ β = {βij}i,j≥0,i+j≤2n, with β00 > 0, the truncated Q-hyperbolic moment problem for β entails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x, y) = 0, such that βij = ∫ yx dμ (0 ≤ i + j ≤ 2n). We prove that β admits a Qrepresenting measure μ (as above) if and only if the associated moment matrix M(n)(β) is positive semidefinite, recursively generated, has a column relation Q(X, Y ) = 0, and the algebraic variety V(β) associated to β satisfies cardV(β) ≥ rankM(n)(β). In this case, rankM(n) ≤ 2n+1; if rankM(n) ≤ 2n, then β admits a rankM(n)-atomic (minimal) Q-representing measure; if rankM(n) = 2n + 1, then β admits a Q-representing measure μ satisfying 2n + 1 ≤ card supp μ ≤ 2n + 2. Mathematics Subject Classification (2000). Primary 47A57, 44A60, 42A70, 30A05; Secondary 15A57, 15-04, 47N40, 47A20. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://homepage.divms.uiowa.edu/~rcurto/tcmp9.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Hospital admission Linear algebra Mathematics Subject Classification Moment matrix Moment problem Neoplasm Metastasis Recursion Suppository |
| Content Type | Text |
| Resource Type | Article |
