Armin Rainer

FWF Stand-alone Project P 26735-N25

Here you can find information on the Stand-alone Project P 26735-N25 "Differential Analysis: Perturbation and Quasianalyticity" supported by the Austrian Science Fund (FWF).

The project was carried out at the Faculty of Mathematics ot the University of Vienna. It started om May 1, 2014 and ended on March 31, 2019.

Project members
  • Armin Rainer (Project leader)
  • Gerhard Schindl
  • David Nenning
  • Sergio Carrillo
Cooperation partners
  • Adam Parusinski (Universite Nice Sophia Antipolis)

  1. G. Schindl, The convenient setting for ultradifferentiable mappings of Beurling- and Roumieu-type defined by a weight matrix, Bull. Belg. Math. Soc. Simon Stevin, 22 (2015), No. 3, 471--510. arXiv:1412.6165.
  2. A. Kriegl, P.W. Michor, A. Rainer, An exotic zoo of diffeomorpism groups on R^n, Annals of Global Analysis and Geometry, 47 (2015), No. 2, 179-222. doi:10.1007/s10455-014-9442-0. arXiv:1404.7033. [PDF]
  3. A. Parusinski, A. Rainer, A new proof of Bronshtein's theorem J. Hyperbolic Differ. Equ., 12 (2015), No. 4, 671-688. doi:10.1142/S0219891615500198. arXiv:1309.2150. [PDF]
  4. G. Schindl, Characterization of ultradifferentiable test functions defined by weight matrices in terms of their Fourier transform, Note di Matematica, 36 (2016), No. 2, 1--35. doi:10.1285/i15900932v36n2p1. arXiv:1502.07387.
  5. A. Rainer, G. Schindl, Equivalence of stability properties for ultradifferentiable function classes , 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]
  6. A. Parusinski, A. Rainer, Regularity of roots of polynomials Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 16 (2016), 481-517. doi:10.2422/2036-2145.201404_014. arXiv:1309.2151. [PDF]
  7. A. Parusinski, A. Rainer, Lifting differentiable curves from orbit spaces Transformation Groups, 21 (2016), No. 1, 153-179. doi:10.1007/s00031-015-9346-5. arXiv:1406.2485. [PDF]
  8. A. Kriegl, P.W. Michor, A. Rainer, The exponential law for spaces of test functions and diffeomorphism groups, Indag. Math. (N.S.), 27 (2016), 225-265. doi:10.1016/j.indag.2015.10.006. arXiv:1411.0483. [PDF]
  9. J. Jimenez-Garrido, J. Sanz, and G. Schindl, Log-convex sequences and nonzero proximate orders, Journal of Mathematical Analysis and Applications 448 (2017), no. 2, 1572--1599. doi:10.1016/j.jmaa.2016.11.069. arXiv:1607.08027.
  10. A. Rainer, G. Schindl, On the Borel mapping in the quasianalytic setting , Math. Scand., 121 (2017), 293-310. doi:10.7146/math.scand.a-97101 arXiv:1509.05565. [PDF]
  11. A. Rainer, G. Schindl, Extension of Whitney jets of controlled growth Math. Nachr., 290 (2017), no. 14-15, 2356-2374. doi:10.1002/mana.201600321. arXiv:1607.01206. [PDF]
  12. A. Parusinski, A. Rainer, Optimal Sobolev regularity of roots of polynomials Ann. Sci. Ec. Norm. Super. (4), 51 (2018), No. 5, 1343-1387. doi:10.24033/asens.2376. arXiv:1506.01512. [PDF]
  13. D.N. Nenning, A. Rainer, On groups of Hölder diffeomorphisms and their regularity Trans. Amer. Math. Soc., 370 (2018), No. 8, 5761-5794. doi:10.1090/tran/7269. arXiv:1612.03390. [PDF]
  14. A. Rainer, Recognizing (ultra)differentiable functions on closed sets, Oberwolfach Reports Volume 14 (2017), Issue 2, 1369-1372. doi:10.4171/OWR/2017/22. [PDF]
  15. A. Rainer, G. Schindl, On the extension of Whitney ultrajets, Studia Math., 245 (2019), No. 3, 255-287. doi:10.4064/sm170906-23-11, arXiv:1709.00932. [PDF]
  16. P.T. Chrusciel, E. Delay, P. Klinger, A. Kriegl, P.W. Michor, A. Rainer, Non-singular spacetimes with a negative cosmological constant: V. Boson stars, Lett. Math. Phys., 108 (2018), No. 9, 2009-2030. doi:10.1007/s11005-018-1062-3, arXiv:1708.02878. [PDF]
  17. M. Bruveris, P.W. Michor, A. Parusinski, A. Rainer, Moser's theorem on manifolds with corners Proc. Amer. Math. Soc. 146 (2018), No. 11, 4889-4897. doi:10.1090/proc/14130, arXiv:1604.07787. [PDF]
  18. D.N. Nenning, A. Rainer, The Trouve group for spaces of test functions, 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]
  19. A. Rainer, G. Schindl, On the extension of Whitney ultrajets, II, Studia Math. 250 (2020), No. 3, 283-295. doi:10.4064/sm180903-12-11, arXiv:1808.10253. [PDF]
  20. A. Rainer, Arc-smooth functions on closed sets, Compositio Mathematica, 155 (2019), 645-680. doi:10.1112/S0010437X19007097 arXiv:1801.08335. [PDF]
  21. A. Rainer, Quasianalytic ultradifferentiability cannot be tested in lower dimensions, Bulletin of the Belgian Mathematical Society - Simon Stevin 26 (2019), 505-517. arXiv:1810.10767. [PDF]
  22. S. Fürdös, D.N. Nenning, A. Rainer, G. Schindl, Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis, Journal of Mathematical Analysis and Applications, 481 (2020), No. 1, doi:10.1016/j.jmaa.2019.123451, arXiv:1904.07634. [PDF]
  23. A. Parusinski, A. Rainer, Selections of bounded variation for roots of smooth polynomials, Selecta Mathematica, doi:10.1007/s00029-020-0538-z. arXiv:1705.10492. [PDF]
  24. S. Carrillo, Summability in a monomial for some classes of singularly perturbed partial differential equations, to appear in Publicacions Matematiques , arXiv:1803.06719.
  25. D.N. Nenning, On time-dependent Besov vector fields and the regularity of their flows, Proc. Amer. Math. Soc., 148 (2020), 623- 638. doi:10.1090/proc/14821. arXiv:1804.07595.
  26. S. Carrillo, J. Mozo-Fernandez, R. Schäfke, Tauberian theorems for k-summability with respect to an analytic germ, Journal of Mathematical Analysis and Applications, 489 (2020), No. 2, doi:10.1016/j.jmaa.2020.124174, arXiv:1903.08898.

  1. S. Carrillo, Bernoulli and Euler numbers from divergent series, arXiv:1903.09228.

  1. D.N. Nenning, ODE-closedness of function spaces and almost analytic extensions of ultradifferentiable functions, defended in January 2020.

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