Dr. Stephan Fackler

  • 2006-2011: Study of Mathematics with minor in Physics at Ulm University
  • 2011-2014: PhD in Mathematics (supervisor: Wolfgang Arendt)
  • 2015-2017: postdoctoral researcher for the project Regularität evolutionärer Probleme mittels Harmonischer Analyse und Operatortheorie (regularity of evolutionary problems via harmonic analysis and operator theory) financed by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft)

Teaching

Lecture notes of previous courses:

Former Courses

Research

During my time as a doctoral and postdoctoral studies my research was focused on the maximal L^p-regularity of abstract Cauchy problems and related issues, such as the holomorphic functional calculus for sectorial operators. During my PhD I was mainly interested in structural questions. In particular, I studied the extrapolation problem for maximal regularity. As a postdoc my focus lied on the maximal regularity of non-autonomous elliptic operators. Moreover, I have done some research on harmonic analysis on Banach spaces (operator-valued Fourier multipliers and Calderón-Zygmund operators).

Further, I am interested in the theory of one parameter semigroups (C_0-semigroups) and in the geometry of Banach spaces, particularly in view of possible applications to semigroup theory.

My research profiles: ORCID | MathSciNet | zbMATH | arXiv

Research Interests

  • Maximal regularity of elliptic operators
  • Sectorial operators and their regularity properties
  • Semigroup theory
  • Functional calculi
  • Harmonic analysis on Banach spaces

Publications and Preprints

  • J. L. Lions' Problem on Maximal Regularity (with W. Arendt & D. Dier), Arch. Math. (Basel) 109 (2017), no. 1, 59-72 (DOI, arXiv)
  • Non-Autonomous Maximal $L^p$-Regularity under Fractional Sobolev Regularity in Time, Preprint (arXiv)
  • Non-Autonomous Maximal Regularity for Forms Given by Elliptic Operators of Bounded Variation, J. Differential Equations 263 (2017), no. 6, 3533–3549 (DOI, arXiv)
  • J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms, Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, 699–709 (DOI, arXiv)
  • Non-Autonomous Maximal L^p-Regularity for Rough Divergence Form Elliptic Operators, Preprint (arXiv)
  • A Short Counterexample to the Inverse Generator Problem on non-Hilbertian Reflexive L^p-spaces, Arch. Math. (Basel) 106 (2016), no. 4, 383–389 (DOI, arXiv)
  • Isometric dilations and H^{\infty} calculus for bounded analytic semigroups and Ritt operators (with C. Arhancet & C. Le Merdy), Trans. Amer. Math. Soc. 369 (2017), no. 10, 6899–6933 (DOI, arXiv)
  • Maximal Regularity: Positive Counterexamples on UMD-Banach Lattices and Exact Intervals for the Negative Solution of the Extrapolation Problem, Proc. Amer. Math. Soc. 144 (2016), no. 5, 2015–2028 (DOI, arXiv)
  • Regularity Properties of Sectorial Operators: Counterexamples and Open Problems, Operator semigroups meet complex analysis, harmonic analysis and mathematical physics, 171–197, Oper. Theory Adv. Appl., 250, Birkhäuser/Springer, Cham, 2015. (DOI, arXiv)
  • On the structure of semigroups on L_p with a bounded H^{\infty}-calculus, Bull. Lond. Math. Soc. 46 (2014), no. 5, 1063–1076 (DOI, arXiv)
  • Local Strong Solutions for the Non-Linear Thermoelastic Plate Equation on Rectangular Domains in L^p-Spaces (with T. Nau), NoDEA Nonlinear Differential Equations Appl. 21 (2014), no. 6, 775–794 (DOI, arXiv)
  • The Kalton-Lancien Theorem Revisited: Maximal Regularity does not extrapolate, J. Funct. Anal. 266 (2014), no. 1, 121–138 (DOI, arXiv)
  • Regularity of semigroups via the asymptotic behaviour at zero, Semigroup Forum 87 (2013), no. 1, 1–17 (DOI, arXiv)
  • An explicit counterexample for the L^p-maximal regularity problem, C. R. Math. Acad. Sci. Paris 351 (2013), no. 1–2, 53–56 (DOI)

Scientific Talks

  • 15 May 2017: Ein neuer Zugang zum Dilatationsresultat von Akcoglu–Sucheston (Forschungsseminar, Ulm)
  • 27 April 2017: A new approach to the Akcoglu–Sucheston dilation theorem for positive contractionson L^p-spaces (Emergent trends of Complex Analysis and Functional Analysis, Będlewo)
  • 14 February 2017: Non-Autonomous Maximal Regularity of Elliptic Operators in Divergence Form (Seminar in Analysis, TU Delft)
  • 16 December 2016: Entropy for Mathematicians (AGFA & IAA Workshop, Blaubeuren)
  • 27 May 2016: Operator Theoretic Tools for Harmonic Analysis and PDE (Workshop Singular integrals and partial differential equations, Helsinki)
  • 22 April 2016: Non-autonomous maximal regularity (Joint Harmonic Analysis and PDE Seminar of the University of Helsinki and Aalto University)
  • 1 February 2016: Bekanntes und Unbekanntes über den H^∞-Kalkül (Oberseminar Funktionalanalysis und Dynamische Systeme, Universität Kiel)
  • 23 November 2015: Banachskalen und nichtautonome Maximale Regularität auf Banachräumen (Forschungsseminar, Ulm)
  • 2 October 2014: Structural Properties of Maximal Regularity (Workshop Functional calculus and Harmonic analysis of semigroups, Besançon)
  • 5 December 2013: Dilatationen und Funktionalkalkül auf L^p- & UMD-Räumen (Forschungsseminar, Ulm)
  • 30 November 2013: Positive Halbgruppen sind generisch für beschränkten H^∞-Kalkül auf L^p (TULKA workshop „40 Jahre Ergodentheorie, 40 Jahre AGFA“, Tübingen)
  • 23 October 2013: On the structure of semigroups on L_p with a bounded H^{\infty}-calculus (Journées du GdR «Analyse Fonctionelle, Harmonique et Probabilités», Lyon)
  • 4 September 2013: A stochastic characterization of maximal parabolic L^p-regularity (Workshop Probability, Analysis and Geometry, Ulm)
  • 6 June 2013: Maximal Regularity does not extrapolate (Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics, Herrnhut)
  • 11 June 2012: Regularity of Semigroups via the Asymptotic Behaviour at Zero (8th Euro-Maghrebian Workshop on Evolution Equations, Lecce)
  • 15 May 2012: Regularität von Halbgruppen durch das asymptotische Verhalten in der Null (TULKA, Karlsruhe)
  • 31 January 2011: B-konvexe Räume sind K-konvex (Forschungsseminar, Ulm)