4 papers · 1 filter
The full shadow of a polynomial II. Vanishing root masses and holes
Christian Hägg, Boris Shapiro
For a complex polynomial , its full shadow is the closure of the set of zeros of all derivatives of all powers , and its limiting core is the Hausdorff limit, as $n\to\inft…
The full shadow of a polynomial I. The limiting core and the transient set
Christian Hägg, Boris Shapiro
The full shadow of a complex polynomial of degree is the closure of all zeros of , , . We prove that it consists of a compact connected l…
Zero asymptotics for successive derivatives of hyperexponential functions with finite essential singularities
Christian Hägg, Boris Shapiro
Pólya's shire theorem identifies the final set of zeros of successive derivatives of an arbitrary meromorphic function with at least one pole with the Voronoi diagram of its finite…
Voronoi limit measures for iterates of constant-coefficient differential operators on rational functions with simple poles
Bosco Nyandwi, Christian Hägg, Celestin Kurujyibwami +1
Bøgvad and Hägg proved that for a rational function with simple poles, the zeros of successive derivatives accumulate on the Voronoi diagram of the pole set, and the normalized zer…