Solution of the truncated hyperbolic moment problem
| dc.creator | Curto, Raul E. | |
| dc.creator | Fialkow, Lawrence A. | |
| dc.date | 2005-07-04 | |
| dc.date.accessioned | 2026-07-07T05:21:22Z | |
| dc.date.available | 2026-07-07T05:21:22Z | |
| dc.description | Let Q(x,y)=0 be an hyperbola in the plane. Given real numbers $β\equivβ^{2n)}=\{β_{ij}\}_{i,j\geq0,i+j\leq2n}$, with $β_{00}>0$, the truncated Q-hyperbolic moment problem for βentails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x,y)=0, such that $β_{ij}=\int y^{i}x^{j} dμ(0\leq i+j\leq2n)$. We prove that βadmits a Q-representing measure μ(as above) if and only if the associated moment matrix $\mathcal{M}(n)(β)$ is positive semidefinite, recursively generated, has a column relation Q(X,Y)=0, and the algebraic variety $\mathcal{V}(β)$ associated to βsatisfies $card\mathcal{V}(β)\geq\rank\mathcal{M}(n)(β)$. In this case, $rank\mathcal{M}(n)\leq2n+1$; if $rank\mathcal{M}(n)\leq2n$, then βadmits a $rank\mathcal{M}(n)$-atomic (minimal) Q-representing measure; if $rank\mathcal{M}(n)=2n+1$, then βadmits a Q-representing measure μsatisfying $2n+1\leqcard suppμ\leq2n+2$. | |
| dc.identifier | https://arxiv.org/abs/math/0507069 | |
| dc.identifier | http://arxiv.org/abs/math/0507069 | |
| dc.identifier | Integral Equations Operator Theory 52(2005), 181-218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75668 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47A57, 44A60, 42A70, 30A05 | |
| dc.title | Solution of the truncated hyperbolic moment problem | |
| dc.type | text |