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The Wronski map and Grassmannians of Real Codimension 2 Subspaces

The Wronski map and Grassmannians of Real Codimension 2 Subspaces We study the map which sends a pair of real polynomials (f0, f1) into their Wronski determinant W(f 0,f 1). This map is closely related to a linear projection from a Grassmannian G R(m,m + 2) to the real projective space ∝ℙ2m . We show that the degree of this projection is +-u((m + 1)/2) where u is the m-th Catalan number. One application of this result is to the problem of describing all real rational functions of given degree m + 1 with prescribed 2m critical points. A related question of control theory is also discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

The Wronski map and Grassmannians of Real Codimension 2 Subspaces

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Publisher
Springer Journals
Copyright
Copyright © 2001 by Heldermann Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03320973
Publisher site
See Article on Publisher Site

Abstract

We study the map which sends a pair of real polynomials (f0, f1) into their Wronski determinant W(f 0,f 1). This map is closely related to a linear projection from a Grassmannian G R(m,m + 2) to the real projective space ∝ℙ2m . We show that the degree of this projection is +-u((m + 1)/2) where u is the m-th Catalan number. One application of this result is to the problem of describing all real rational functions of given degree m + 1 with prescribed 2m critical points. A related question of control theory is also discussed.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References