Armin Rainer

Publications

You may download this list of publications in PDF format. Most articles are also available on arXiv.org.


Preprints and Work in Progress
  • Interpolation of derivatives and ultradifferentiable regularity, with Gerhard Schindl, arXiv:2312.07020. [PDF]
  • On real analytic functions on closed subanalytic domains, arXiv:2311.03014. [PDF]
  • Perturbation theory of polynomials and linear operators, with Adam Parusinski, arXiv:2308.01299. [PDF]
  • Uniform extension of definable $C^{m,\omega}$-Whitney jets, with Adam Parusinski, arXiv:2306.09156. [PDF]
Publications in refereed Journals and Proceedings
  1. Definable Lipschitz selections for affine-set valued maps, with Adam Parusinski, accepted for publication in Israel Journal of Mathematics, arXiv:2306.09155. [PDF]
  2. 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]
  3. Arc-smooth functions and cuspidality of sets, accepted for publication in Journal d'Analyse Mathématique. arXiv:2112.14163. [PDF]
  4. 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]
  5. 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]
  6. Hölder-Zygmund classes on smooth curves, Z. Anal. Anwend., 41, no. 1 (2022), 189-209. doi:10.4171/zaa/1704, arXiv:2203.04191. [PDF]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. Roots of Garding hyperbolic polynomials, Proc. Amer. Math. Soc., 150 (2022), No. 6, 2433-2446. doi:10.1090/proc/15634, arXiv:2012.01077. [PDF]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. Arc-smooth functions on closed sets, Compositio Mathematica, 155 (2019), 645-680. doi:10.1112/S0010437X19007097 arXiv:1801.08335. [PDF]
  19. 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]
  20. 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]
  21. 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]
  22. 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]
  23. 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]
  24. Recognizing (ultra)differentiable functions on closed sets, Oberwolfach Reports Volume 14 (2017), Issue 2, 1369-1372. doi:10.4171/OWR/2017/22. [PDF]
  25. 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]
  26. 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]
  27. 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]
  28. 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]
  29. 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]
  30. 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]
  31. 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]
  32. 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]
  33. 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]
  34. 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]
  35. An exotic zoo of diffeomorpism 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]
  36. 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]
  37. 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]
  38. 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]
  39. 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]
  40. 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]
  41. 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. ESI Preprint 1921. arXiv:math.FA/0611506. [PDF]
  42. 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]
  43. 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]
  44. 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]
  45. 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]
  46. 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]
  47. 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]
  48. 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]
  49. 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: arXiv:0711.3163. [PDF]
  50. Orbit projections of proper Lie groupoids as fibrations, Czechoslovak Math. J. 59 (2009), No. 3, 591--594. arXiv:0712.0706. [PDF]
  51. Orbit projections as fibrations, Czechoslovak Math. J. 59 (2009), No. 2, 529--538. ESI Preprint 1854, arXiv:math.DG/0610513. [PDF]
  52. 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, ESI Preprint 1415, arXiv:math.AG/0312030. [PDF]
  53. Choosing roots of polynomials with symmetries smoothly, with M. Losik, Revista Matemática Complutense 20 (2007), No. 2, 267--291, ESI Preprint 1792, arXiv:math.CA/0603660. [PDF]
  54. Singular Poisson reduction of cotangent bundles, with S. Hochgerner, Revista Matemática Complutense 19 (2006), No. 2, 431--466, ESI Preprint 1681, arXiv:math.SG/0508455. [PDF]
  55. 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, ESI Preprint 1806, arXiv:math.RT/0504101. [PDF]
  56. 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, ESI Preprint 1459, arXiv:math.RT/0402222. [PDF]
Research Monograph
  • Perturbation of hyperbolic polynomials and related lifting problems, corrected and extended version of the doctoral thesis as monograph, in preparation. [PDF]
Theses
  • Perturbation theory for polynomials and linear operators & The convenient setting for Denjoy--Carleman differentiable mappings, habilitation thesis, University of Vienna, 2010. [PDF]
  • Choosing roots of polynomials smoothly and lifting smooth curves over invariants, doctoral thesis, University of Vienna, 2004. [PDF]
  • Zerlegungsgleichheit von Kreis und Quadrat, diploma thesis (in German), University of Salzburg, 2002. [PDF]



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