The Schur transformation for Nevanlinna functions: operator representations, resolvent matrices, and orthogonal polynomials
| dc.creator | Alpay, D. | |
| dc.creator | Dijksma, A. | |
| dc.creator | Langer, H. | |
| dc.date | 2007-11-27 | |
| dc.date.accessioned | 2026-07-07T08:45:22Z | |
| dc.date.available | 2026-07-07T08:45:22Z | |
| dc.description | A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function $n$ with a suitable asymptotic expansion at $\infty$, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation $p$ times we find a Nevanlinna function $n_p$ which is a fractional linear transformation of the given function $n$. The main results concern the effect of this transformation to the realizations of $n$ and $n_p$, by which we mean their representations through resolvents of self-adjoint operators in Hilbert space. Our tools are block operator matrix representations, $u$--resolvent matrices, and reproducing kernel Hilbert spaces. | |
| dc.description | 37 pages | |
| dc.identifier | https://arxiv.org/abs/0711.4236 | |
| dc.identifier | http://arxiv.org/abs/0711.4236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142942 | |
| dc.subject | Functional Analysis | |
| dc.subject | Complex Variables | |
| dc.subject | 47A57; 47B32; 42C05; 30E05 | |
| dc.title | The Schur transformation for Nevanlinna functions: operator representations, resolvent matrices, and orthogonal polynomials | |
| dc.type | text |