A note on polydegree (n, 1) rational inner functions, slice matrices, and singularities

We analyze certain compositions of rational inner functions in the unit polydisk D d with polydegree ( n , 1), n ∈ N d - 1 , and isolated singularities in T d . Provided an irreducibility condition is met, such a composition is shown to be a rational inner function with singularities in precisely th...

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Bibliographic Details
Published in:Archiv der Mathematik 2023-02, Vol.120 (2), p.171-181
Main Author: Sola, Alan
Format: Article
Language:English
Subjects:
Composition
Derivative integrability
Mathematics
Mathematics and Statistics
Rational inner function
Singularity (mathematics)
Slice matrix
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Summary:We analyze certain compositions of rational inner functions in the unit polydisk D d with polydegree ( n , 1), n ∈ N d - 1 , and isolated singularities in T d . Provided an irreducibility condition is met, such a composition is shown to be a rational inner function with singularities in precisely the same location as those of the initial function, and with quantitatively controlled properties. As an application, we answer a d -dimensional version of a question posed in Bickel et al. (Am J Math 144: 1115–1157, 2022) in the affirmative.
ISSN:0003-889X
1420-8938
1420-8938
DOI:10.1007/s00013-022-01812-3