Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4672882 | Indagationes Mathematicae | 2012 | 11 Pages |
Abstract
A finite sequence c0,…,ckc0,…,ck of complex numbers is the set of trigonometric moments of a measure dμ=∣Pk(eiθ)∣−2dθdμ=∣Pk(eiθ)∣−2dθ with Pk(z)Pk(z) a polynomial of degree kk, zero-free in |z|≤1|z|≤1, providing only that the Hermitian Toeplitz matrix having c0,…,ckc0,…,ck as its top row is positive-definite. The analogous representation in two dimensions for a rectangular array of numbers requires additional conditions, discovered by J.S. Geronimo and H.J. Woerdeman. We use orthogonal decomposition to give an alternate proof of their important result.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
H.J. Landau, Zeph Landau,