A. Parusiński

activity

19942026

most citedCharacteristic Classes of Hypersurfaces and Characteristic Cycles

93 citations · 180 across the 39 of their papers we have counts for

collaborators

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6 papers · 1 filter

math.CA2020

Sobolev Lifting over Invariants

Adam Parusiński, Armin Rainer

We prove lifting theorems for complex representations $V$ of finite groups $G$ . Let $σ = (σ_{1}, \dots, σ_{n})$ be a minimal system of homogeneous basic invariants and let $d$ be their max…

math.CA2017★ 3 cited

Selections of bounded variation for roots of smooth polynomials

Adam Parusinski, Armin Rainer

We prove that the roots of a smooth monic polynomial with complex-valued coefficients defined on a bounded Lipschitz domain $Ω$ in $R^{m}$ admit a parameterization by functio…

math.CA2015★ 1 cited

Optimal Sobolev regularity of roots of polynomials

Adam Parusinski, Armin Rainer

We study the regularity of the roots of complex univariate polynomials whose coefficients depend smoothly on parameters. We show that any continuous choice of the roots of a $C^{n-…

math.CA2013★ 15 cited

Regularity of roots of polynomials

Adam Parusinski, Armin Rainer

We show that smooth curves of monic complex polynomials $P_{a} (Z) = Z^{n} + \sum_{j = 1}^{n} a_{j} Z^{n - j}$ , $a_{j} : I \to C$ with $I \subset R$ a compact interval, have absolute…

math.CA2013★ 11 cited

A new proof of Bronshtein's theorem

Adam Parusinski, Armin Rainer

We give a new self-contained proof of Bronshtein's theorem, that any continuous root of a $C^{n - 1, 1}$ -family of monic hyperbolic polynomials of degree $n$ is locally Lipschitz, and…

math.CA2013★ 3 cited

Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings

Jean-Philippe Rolin, Adam Parusinski

Consider quasianalytic local rings of germs of smooth functions closed under composition, implicit equation, and monomial division. We show that if the Weierstrass Preparation Theo…