A Hilbert Lemniscate Theorem in C^2
| dc.creator | Bloom, T. | |
| dc.creator | Levenberg, N. | |
| dc.creator | Lyubarskii, Yu. | |
| dc.date | 2006-07-22 | |
| dc.date.accessioned | 2026-07-07T07:20:49Z | |
| dc.date.available | 2026-07-07T07:20:49Z | |
| dc.description | For a regular, compact, polynomially convex circled set K in C^2, we construct a sequence of pairs {P_n,Q_n} of homogeneous polynomials in two variables with deg P_n = deg Q_n = n such that the sets K_n: = {(z,w) \in C^2 : |P_n(z,w)| \leq 1, |Q_n(z,w)| \leq 1} approximate K and the normalized counting measures {μ_n} associated to the finite set {P_n = Q_n = 1} converge to the pluripotential-theoretic Monge-Ampere measure for K. The key ingredient is an approximation theorem for subharmonic functions of logarithmic growth in one complex variable. | |
| dc.identifier | https://arxiv.org/abs/math/0607574 | |
| dc.identifier | http://arxiv.org/abs/math/0607574 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115088 | |
| dc.subject | Complex Variables | |
| dc.title | A Hilbert Lemniscate Theorem in C^2 | |
| dc.type | text |