A pre-order and an equivalence relation on Schur class functions and their invariance under linear fractional transformations
Functional Analysis
2014-08-05 v1
Abstract
Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation on the set of operator-valued Schur class functions are introduced and the behavior of Redheffer linear fractional transformations (LFTs) with respect to these relations is studied. In particular, it is shown that Redheffer LFTs preserve the equivalence relation, but not necessarily the pre-order. The latter does occur under some additional assumptions on the coefficients in the Redheffer LFT.
Keywords
Cite
@article{arxiv.1408.0523,
title = {A pre-order and an equivalence relation on Schur class functions and their invariance under linear fractional transformations},
author = {S. ter Horst},
journal= {arXiv preprint arXiv:1408.0523},
year = {2014}
}
Comments
29 pages