午夜探花

Institute of Applied Analysis

Dr. Stephan Fackler

  • 2006-2011: Study of Mathematics with minor in Physics at 午夜探花
  • 2011-2014: PhD in Mathematics (supervisor: Wolfgang Arendt)
  • 2015-2017: postdoctoral researcher for the project (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:

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 Calder贸n-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: | | |

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

  • J. L. Lions' Problem on Maximal Regularity (with W. Arendt & D. Dier), Arch. Math. (Basel) 109 (2017), no. 1, 59-72 (, )
  • Non-Autonomous Maximal $L^p$-Regularity under Fractional Sobolev Regularity in Time, Preprint ()
  • Non-Autonomous Maximal Regularity for Forms Given by Elliptic Operators of Bounded Variation, J. Differential Equations 263 (2017), no. 6, 3533鈥�3549 (, )
  • J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms, Ann. Inst. H. Poincar茅 Anal. Non Lin茅aire 34 (2017), no. 3, 699鈥�709 (, )
  • Non-Autonomous Maximal L^p-Regularity for Rough Divergence Form Elliptic Operators, Preprint ()
  • A Short Counterexample to the Inverse Generator Problem on non-Hilbertian Reflexive L^p-spaces, Arch. Math. (Basel) 106 (2016), no. 4, 383鈥�389 (, )
  • 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鈥�6933 (, )
  • 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鈥�2028 (, )
  • Regularity Properties of Sectorial Operators: Counterexamples and Open Problems, Operator semigroups meet complex analysis, harmonic analysis and mathematical physics, 171鈥�197, Oper. Theory Adv. Appl., 250, Birkh盲user/Springer, Cham, 2015. (, )
  • On the structure of semigroups on L_p with a bounded H^{\infty}-calculus, Bull. Lond. Math. Soc. 46 (2014), no. 5, 1063鈥�1076 (, )
  • 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鈥�794 (, )
  • The Kalton-Lancien Theorem Revisited: Maximal Regularity does not extrapolate, J. Funct. Anal. 266 (2014), no. 1, 121鈥�138 (, )
  • Regularity of semigroups via the asymptotic behaviour at zero, Semigroup Forum 87 (2013), no. 1, 1鈥�17 (, )
  • An explicit counterexample for the L^p-maximal regularity problem, C. R. Math. Acad. Sci. Paris 351 (2013), no. 1鈥�2, 53鈥�56 ()

  • 15 May 2017: Ein neuer Zugang zum Dilatationsresultat von Akcoglu鈥揝ucheston (Forschungsseminar, Ulm)
  • 27 April 2017: A new approach to the Akcoglu鈥揝ucheston dilation theorem for positive contractionson L^p-spaces (Emergent trends of Complex Analysis and Functional Analysis, B臋dlewo)
  • 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 眉ber den 贬镑鈭�-碍补濒办眉濒 (Oberseminar Funktionalanalysis und Dynamische Systeme, Universit盲t Kiel)
  • 23 November 2015: Banachskalen und nichtautonome Maximale Regularit盲t auf Banachr盲umen (Forschungsseminar, Ulm)
  • 2 October 2014: Structural Properties of Maximal Regularity (Workshop Functional calculus and Harmonic analysis of semigroups, Besan莽on)
  • 5 December 2013: Dilatationen und Funktionalkalk眉l auf L^p- & UMD-R盲umen (Forschungsseminar, Ulm)
  • 30 November 2013: Positive Halbgruppen sind generisch f眉r beschr盲nkten 贬镑鈭�-碍补濒办眉濒 auf L^p (TULKA workshop 鈥�40 Jahre Ergodentheorie, 40 Jahre AGFA鈥�, T眉bingen)
  • 23 October 2013: On the structure of semigroups on L_p with a bounded H^{\infty}-calculus (Journ茅es du GdR 芦Analyse Fonctionelle, Harmonique et Probabilit茅s禄, 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: Regularit盲t von Halbgruppen durch das asymptotische Verhalten in der Null (TULKA, Karlsruhe)
  • 31 January 2011: B-konvexe R盲ume sind K-konvex (Forschungsseminar, Ulm)