We investigate the regularity of functions $\tau$ of one variable such that $P(t,\tau(t))=0$, where $P(t,x)$ is a given polynomial of degree $m$ in $x$ whose coefficients are functions of class $C^{m^2!}$ of $t$. We show that there is a complete family of roots that are absolutely continuous functions of $t$; indeed, we prove that any complete family of continuous roots has this property.
On the regularity of the roots of hyperbolic polynomials
PERNAZZA, LUDOVICO
2012-01-01
Abstract
We investigate the regularity of functions $\tau$ of one variable such that $P(t,\tau(t))=0$, where $P(t,x)$ is a given polynomial of degree $m$ in $x$ whose coefficients are functions of class $C^{m^2!}$ of $t$. We show that there is a complete family of roots that are absolutely continuous functions of $t$; indeed, we prove that any complete family of continuous roots has this property.File in questo prodotto:
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