You may download this list of publications in PDF format. Most articles are also available on arXiv.org.
Preprints and Work in Progress
- On spaces of arc-smooth maps, arXiv:2503.07023. [PDF]
- On the continuity of the solution map for polynomials, with Adam Parusinski, arXiv:2410.01326. [PDF]
- Continuity of the solution map for hyperbolic polynomials, with Adam Parusinski, arXiv:2410.01321. [PDF]
Publications in refereed Journals and Proceedings
accepted for publication
- Definable Lipschitz selections for affine-set valued maps, with Adam Parusinski, accepted for publication in Israel Journal of Mathematics, arXiv:2306.09155. [PDF]
2025
- Interpolation of derivatives and ultradifferentiable regularity, with Gerhard Schindl, Math. Nach. 298 (2025), no. 2, 617-635. doi:10.1002/mana.202300567. arXiv:2312.07020. [PDF]
- Perturbation theory of polynomials and linear operators, with Adam Parusinski, Handbook of Geometry and Topology of Singularities, VII, Springer Nature. doi:10.1007/978-3-031-68711-2_3. arXiv:2308.01299. [PDF]
2024
- Uniform extension of definable $C^{m,\omega}$-Whitney jets, with Adam Parusinski, Pacific Journal of Mathematics, 330-2 (2024), 317-353. doi:10.2140/pjm.2024.330.317. arXiv:2306.09156. [PDF]
- On real analytic functions on closed subanalytic domains, Archiv der Mathematik 122 (2024), 639-650. doi:10.1007/s00013-024-01983-1. arXiv:2311.03014. [PDF]
- Arc-smooth functions and cuspidality of sets, Journal d’Analyse Mathématique (2024). doi:10.1007/s11854-024-0337-0. arXiv:2112.14163. [PDF]
2023
- Quantitative tame properties of differentiable functions with controlled derivatives, Nonlinear Analysis 237 (2023), 113372. doi:10.1016/j.na.2023.113372, arXiv:2208.04006. [PDF]
- The Borel map in the mixed Beurling setting, with David Nenning and Gerhard Schindl, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 117 (2023), Article number 40. doi:10.1007/s13398-022-01372-9. arXiv:2205.08195. Read here: https://rdcu.be/c1uHx. [PDF]
2022
- On optimal solutions of the Borel problem in the Roumieu case, with David Nenning and Gerhard Schindl, Bull. Belg. Math. Soc. Simon Stevin 29 (2022), no. 4, 509-531. doi:10.36045/j.bbms.220322. arXiv:2112.08463. [PDF]
- Hölder-Zygmund classes on smooth curves, Z. Anal. Anwend. 41, no. 1 (2022), 189-209. doi:10.4171/zaa/1704. arXiv:2203.04191. [PDF]
- Nonlinear conditions for ultradifferentiability: a uniform approach, with David Nenning and Gerhard Schindl, J. Geom. Anal. 32, 171 (2022). doi:10.1007/s12220-022-00914-2. arXiv:2109.07795. Read here: https://rdcu.be/cJ2w4. [PDF]
- Ultradifferentiable extension theorems: a survey, Expositiones Mathematicae 40 (2022), No. 3, 679-757. doi:10.1016/j.exmath.2021.12.001. arXiv:2107.01061. [PDF]
- Roots of Garding hyperbolic polynomials, Proc. Amer. Math. Soc. 150 (2022), No. 6, 2433-2446. doi:10.1090/proc/15634. arXiv:2012.01077. [PDF]
2021
- Nonlinear conditions for ultradifferentiability, with David Nenning and Gerhard Schindl, J. Geom. Anal. 31, 12264-12287 (2021). doi:10.1007/s12220-021-00718-w. arXiv:2102.03871. [PDF]
- Ultraholomorphic sectorial extensions of Beurling type, with David Nenning and Gerhard Schindl, Annals of Functional Analysis 12, 45 (2021). doi:10.1007/s43034-021-00124-x. arXiv:2012.12332. [PDF]
- Sobolev lifting over invariants, with Adam Parusinski, SIGMA Symmetry, Integrability and Geometry: Methods and Applications 17 (2021), 037, 31 pages. doi:10.3842/SIGMA.2021.037. arXiv:2003.01967. [PDF]
- On the extension of Whitney ultrajets of Beurling type, Results in Mathematics 76, 36 (2021). doi:10.1007/s00025-021-01347-z. arXiv:2011.02178. [PDF]
- Ultradifferentiable Chevalley theorems and isotropic functions, Annali di Matematica Pura ed Applicata 200, No. 2, 491-504 (2021), doi:10.1007/s10231-020-01003-3. arXiv:1912.09114. [PDF]
2020
- Selections of bounded variation for roots of smooth polynomials, with Adam Parusinski, Selecta Mathematica 26, 13 (2020), doi:10.1007/s00029-020-0538-z. arXiv:1705.10492. [PDF]
- Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis, with Stefan Fürdös, David Nicolas Nenning, and Gerhard Schindl, Journal of Mathematical Analysis and Applications, 481 (2020), No. 1. doi:10.1016/j.jmaa.2019.123451. arXiv:1904.07634. [PDF]
- On the extension of Whitney ultrajets, II, with Gerhard Schindl, Studia Math. 250 (2020), No. 3, 283-295. doi:10.4064/sm180903-12-11. arXiv:1808.10253. [PDF]
2019
- Quasianalytic ultradifferentiability cannot be tested in lower dimensions, Bulletin of the Belgian Mathematical Society – Simon Stevin 26 (2019), 505-517. doi:10.36045/bbms/1576206353. arXiv:1810.10767. [PDF]
- Arc-smooth functions on closed sets, Compositio Mathematica, 155 (2019), 645-680. doi:10.1112/S0010437X19007097. arXiv:1801.08335. [PDF]
- The Trouve group for spaces of test functions, with David Nicolas Nenning, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 113 (2019), No. 3, 1799-1822. doi:10.1007/s13398-018-0581-1. arXiv:1711.01196. [PDF]
- On the extension of Whitney ultrajets, with Gerhard Schindl, Studia Math., 245 (2019), No. 3, 255-287. doi:10.4064/sm170906-23-11, arXiv:1709.00932. [PDF]
2018
- Moser’s theorem on manifolds with corners with Martins Bruveris, Peter W. Michor, and Adam Parusinski, Proc. Amer. Math. Soc. 146 (2018), No. 11, 4889-4897. doi:10.1090/proc/14130. arXiv:1604.07787. [PDF]
- Non-singular spacetimes with a negative cosmological constant: V. Boson stars, Piotr T. Chrusciel, Erwann Delay, Paul Klinger, with an Appendix by Andreas Kriegl, Peter W. Michor, and Armin Rainer, Lett. Math. Phys., 108 (2018), No. 9, 2009-2030. doi:10.1007/s11005-018-1062-3, arXiv:1708.02878. [PDF]
- On groups of Hölder diffeomorphisms and their regularity with David Nicolas Nenning, Trans. Amer. Math. Soc., 370 (2018), No. 8, 5761-5794. doi:10.1090/tran/7269. arXiv:1612.03390. [PDF]
- Optimal Sobolev regularity of roots of polynomials with Adam Parusinski, Ann. Sci. Ec. Norm. Super. (4), 51 (2018), No. 5, 1343-1387. doi:10.24033/asens.2376. arXiv:1506.01512. [PDF]
2017
- Recognizing (ultra)differentiable functions on closed sets, Oberwolfach Reports Volume 14 (2017), Issue 2, 1369-1372. doi:10.4171/OWR/2017/22. [PDF]
- Extension of Whitney jets of controlled growth with Gerhard Schindl, Math. Nachr., 290 (2017), no. 14-15, 2356-2374. doi:10.1002/mana.201600321. arXiv:1607.01206. [PDF]
- On the Borel mapping in the quasianalytic setting, with Gerhard Schindl, Math. Scand., 121 (2017), 293-310. doi:10.7146/math.scand.a-97101. arXiv:1509.05565. [PDF]
2016
- The exponential law for spaces of test functions and diffeomorphism groups, with A. Kriegl and P.W. Michor, Indag. Math. (N.S.), 27 (2016), 225-265. doi:10.1016/j.indag.2015.10.006. arXiv:1411.0483. [PDF]
- Lifting differentiable curves from orbit spaces with Adam Parusinski, Transformation Groups, 21 (2016), No. 1, 153-179. doi:10.1007/s00031-015-9346-5. arXiv:1406.2485. [PDF]
- Regularity of roots of polynomials with Adam Parusinski, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 16 (2016), 481-517. doi:10.2422/2036-2145.201404_014. arXiv:1309.2151. [PDF]
- Equivalence of stability properties for ultradifferentiable function classes , with Gerhard Schindl, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 110 (2016), No. 1, 17-32. doi:10.1007/s13398-014-0216-0. arXiv:1407.6673. [PDF]
2015
- The convenient setting for Denjoy-Carleman differentiable mappings of Beurling and Roumieu type, with A. Kriegl and P.W. Michor, Revista Matemática Complutense, 28 (2015), No. 3, 549-597. doi:10.1007/s13163-014-0167-1. arXiv:1111.1819. [PDF]
- A new proof of Bronshtein’s theorem with Adam Parusinski, J. Hyperbolic Differ. Equ., 12 (2015), No. 4, 671-688. doi:10.1142/S0219891615500198. arXiv:1309.2150. [PDF]
- An exotic zoo of diffeomorphism groups on R^n, with A. Kriegl and P.W. Michor, Annals of Global Analysis and Geometry, 47 (2015), No. 2, 179-222. doi:10.1007/s10455-014-9442-0. arXiv:1404.7033. [PDF]
2014
- Composition in ultradifferentiable classes, with Gerhard Schindl, Studia Math., 224 (2014), No. 2, 97-131. doi:10.4046/sm224-2-1. arXiv:1210.5102. [PDF]
- Differentiable roots, eigenvalues, and eigenvectors, Israel J. Math., 201 (2014), No. 1, 99-122. doi:10.1007/s11856-014-0007-5. arXiv:1211.4124. [PDF]
2013
- Perturbation theory for normal operators, Trans. Amer. Math. Soc., 365 (2013), 5545-5577. doi:10.1090/S0002-9947-2013-05854-0. arXiv:1111.4475. [PDF]
2012
- Addendum to: ”Lifting smooth curves over invariants for representations of compact Lie groups, III” [J. Lie Theory 16 (2006), No. 3, 579–600.], with A. Kriegl, M. Losik and P.W. Michor, J. Lie Theory 22 (2012), No. 1, 245-249. arXiv:1106.6041. [PDF]
- Many parameter Hölder perturbation of unbounded operators, with A. Kriegl and P.W. Michor, Math. Ann. 353 (2012), 519-522. doi:10.1007/s00208-011-0693-9. arXiv:math.FA/0611506. [PDF]
- Lifting quasianalytic mappings over invariants, Canad. J. Math., 64 (2012), No. 2, 409-428. doi:10.4153/CJM-2011-049-0. arXiv:1007.0836. [PDF]
- A generalization of Puiseux’s theorem and lifting curves over invariants, with M. Losik and P.W. Michor, Revista Matemática Complutense, 25 (2012), No. 1, 139-155. doi:10.1007/s13163-011-0062-y. arXiv:0904.2068. [PDF]
2011
- Denjoy-Carleman differentiable perturbation of polynomials and unbounded operators, with A. Kriegl and P.W. Michor, Integral Equations and Operator Theory 71 (2011), No. 3, 407-416. doi:10.1007/s00020-011-1900-5. arXiv:0910.0155. [PDF]
- The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings, with A. Kriegl and P.W. Michor, Journal of Functional Analysis 261 (2011), 1799-1834. doi:10.1016/j.jfa.2011.05.019. arXiv:0909.5632. [PDF]
- Quasianalytic multiparameter perturbation of polynomials and normal matrices, Trans. Amer. Math. Soc. 363 (2011), No. 9, 4945-4977. doi:10.1090/S0002-9947-2011-05311-0. arXiv:0905.0837. [PDF]
- Smooth roots of hyperbolic polynomials with definable coefficients, Israel J. Math. 184 (2011), No. 1, 157-182. doi:10.1007/s11856-011-0063-z. arXiv:0904.4164. [PDF]
2009
- Perturbation of complex polynomials and normal operators, Math. Nach. 282 (2009), No. 12, 1623-1636. doi:10.1002/mana.200910837. arXiv:math.CA/0611633. [PDF]
- The convenient setting for non-quasianalytic Denjoy-Carleman differentiable mappings, with A. Kriegl and P.W. Michor, Journal of Functional Analysis 256 (2009), 3510-3544. doi:10.1016/j.jfa.2009.03.003. arXiv:0804.2995. [PDF]
- Invariant functions in Denjoy-Carleman classes, Annals of Global Analysis and Geometry 35 (2009), No. 3, 249-266. doi:10.1007/s10455-008-9135-7. A longer version is available at arXiv:0711.3163. [PDF]
- Orbit projections of proper Lie groupoids as fibrations, Czechoslovak Math. J. 59 (2009), No. 3, 591-594. doi:10.1007/s10587-009-0053-z. arXiv:0712.0706. [PDF]
- Orbit projections as fibrations, Czechoslovak Math. J. 59 (2009), No. 2, 529-538. doi:10.1007/s10587-009-0035-1. arXiv:math.DG/0610513. [PDF]
2008
- Lifting mappings over invariants of finite groups, with A. Kriegl, M. Losik, and P.W. Michor, Acta Math. Univ. Comenianae 77 (2008), No. 1, 93-122, arXiv:math.AG/0312030. [PDF]
2007
- Choosing roots of polynomials with symmetries smoothly, with M. Losik, Revista Matemática Complutense 20 (2007), No. 2, 267-291. doi:10.5209/rev_REMA.2007.v20.n2.16475. arXiv:math.CA/0603660. [PDF]
2006
- Singular Poisson reduction of cotangent bundles, with S. Hochgerner, Revista Matemática Complutense 19 (2006), No. 2, 431-466. doi:10.5209/rev_REMA.2006.v19.n2.16607. arXiv:math.SG/0508455. [PDF]
- Lifting smooth curves over invariants for representations of compact Lie groups, III, with A. Kriegl, M. Losik, and P.W. Michor, J. Lie Theory 16 (2006), No. 3, 579-600. arXiv:math.RT/0504101. [PDF]
2005
- Lifting smooth curves over invariants for representations of compact Lie groups, II, with A. Kriegl, M. Losik, and P.W. Michor, J. Lie Theory 15 (2005), No. 1, 227-234. arXiv:math.RT/0402222. [PDF]