3 citations · 12 across the 8 of their papers we have counts for
4 papers · 1 filter
On solutions of linear equations with polynomial coefficients
Janusz Adamus, Hadi Seyedinejad
We show that a linear functional equation with polynomial coefficients need not admit an arc-analytic solution even if it admits a continuous semialgebraic one. We also show that s…
Extensions of arc-analytic functions
Janusz Adamus, Hadi Seyedinejad
We prove that every arc-analytic semialgebraic function on an arc-symmetric set admits an arc-analytic semialgebraic extension to the whole ambient Euclidean space.
Decomposition of sets in real algebraic geometry
Hadi Seyedinejad
We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposit…
A proof of Kurdyka's conjecture on arc-analytic functions
Janusz Adamus, Hadi Seyedinejad
We prove a conjecture of Kurdyka stating that every arc-symmetric semialgebraic set is precisely the zero locus of an arc-analytic semialgebraic function. This implies, in particul…