A note on homotopies of rational matrix inner functions
We show that when <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m greater-than n"> <mml:semantics> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>></mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">m>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , the space of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m times n"> <mml:semantics> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo> × </mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">m\times n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -matrix-valued rational inner functions in the disk is path connected.
Authors
- Michael T. Jury
Institutions
- University of Florida (US)
Publication Details
- Journal
- Proceedings of the American Mathematical Society
- Published
- 2026-01-15
- DOI
- https://doi.org/10.1090/proc/17549
- Primary Topic
- Analytic and geometric function theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00