Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4641019 | Journal of Computational and Applied Mathematics | 2009 | 9 Pages |
Abstract
Let uu be a Hermitian linear functional defined in the linear space of Laurent polynomials and FF its corresponding Carathéodory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for FF, zAF′=BF2+CF+DzAF′=BF2+CF+D, and a distributional equation for uu, D(Au)=B̃u2+C̃u+H̃L, where LL is the Lebesgue functional, and the polynomials B̃,C̃,H̃ are defined in terms of the polynomials A,B,C,DA,B,C,D.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
A. Branquinho, M.N. Rebocho,