Dr.  Marc Hovemann

Philipps-Universität
Fachbereich Mathematik und Informatik
AG Numerik und Optimierung

Important note: This website will not be updated after 1.9.2024 anymore. Please visit my new website.

Research Interests:

• quarklet characterizations for function spaces
• adaptive quarklet tree approximation
• quarklets as multiwavelets
• function spaces (especially Besov-type and Triebel-Lizorkin-type spaces)
• equivalent quasi-norms for function spaces
• characterizations for function spaces in terms of higher-order differences
• Hedberg-Netrusov approach to function spaces
• interpolation and composition operators

PhD Thesis:

• M. Hovemann: Smoothness Morrey Spaces and Differences: Characterizations and Applications
  (Supervisor: Prof. W. Sickel, 2021) [PDF]

Publications and Preprints:

• M. Hovemann, M. Weimar: Oscillations and differences in Besov-Morrey and Besov-type spaces.
  arXiv:2405.20662 [PDF]
• M. Hovemann: Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products.
  arXiv:2403.14388 [PDF]
• M. Hovemann, M. Weimar: Oscillations and differences in Triebel-Lizorkin-Morrey spaces.
  Rev. Mat. Complut. [PDF]
• S. Dahlke, M. Hovemann, T. Raasch, D. Vogel: Adaptive Quarklet Tree Approximation.
  arXiv:2301.04111 [PDF]
• M. Hovemann, A. Kopsch, T. Raasch, D. Vogel: B-Spline Quarklets and Biorthogonal Multiwavelets.
  Int. J. Wavelets Multiresolut. Inf. Process. , published online. [PDF]
• M. Hovemann, S. Dahlke: Quarklet Characterizations for Triebel-Lizorkin spaces.
  J. Approx. Theory 295, 105968, 2023. [PDF]
• M. Hovemann: Triebel-Lizorkin-Morrey Spaces and Differences.
  Math. Nachr. 295, 725-761, 2022. [PDF]
• M. Hovemann: Besov-Morrey spaces and differences.
  Math. Rep. (Bucur.), 23(73), No. 1-2, 175-192, 2021. [PDF]
• M. Hovemann: Besov-Morrey spaces and differences (extended version).
  arXiv:2010.10856 [PDF]
• M. Hovemann: Truncation in Besov-Morrey and Triebel-Lizorkin-Morrey spaces.
  Nonlinear Anal., 204, 112239, 2021. [PDF]
• M. Hovemann, W. Sickel: Besov-type spaces and differences.
  Eurasian Math. J.13(1), 25-56, 2020. [PDF]
• C. Zhuo, M. Hovemann, W. Sickel: Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains.
  Anal. Geom. Metr. Spaces, 8, 268-304, 2020. [PDF]

Awards and Funding :

• DFG Project "Adaptive Quarklet Methods for the numerical Solution of Elliptic Partial Differential Equations with exponential Convergence"
  ( since 1.9.2023 )
• Promotionspreis des Dekans 2022
  ( 13.1.2023 , FSU Jena)
• Auszeichnung für herausragende Leistungen als Übungsleiter für das Fach Analysis 2
  ( 20.11.2020 , FSU Jena , verliehen von der Physikalisch-Astronomischen Fakultät )
• Landesgraduiertenstipendium der FSU Jena
  ( 1.3.2018 - 28.2.2021 , zur Erstellung der Promotion )
• Examenspreis des Dekans 2018
  ( 2.11.2018 , FSU Jena , wegen der Masterarbeit "Strichartz-Charakterisierungen von F^s_{p,q}" )

Talks (in Seminars or Conferences):

• Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products
  ( 31.5.2024 , function spaces seminar Jena )
• Multivariate Quarklets in the Context of Bessel-Potential Spaces on Unit Cubes
  ( 9.2.2024 , Rhein-Ruhr-Workshop , Bestwig )
• Poster: "Adaptive near-best Quarklet Tree Approximation"
  ( 26.9.2023 , Two-day workshop on Approximation Theory , Giessen )
• Triebel-Lizorkin-Morrey Spaces and Oscillations
  ( 28.8.2023 , Siegmundsburg seminar )
• Triebel-Lizorkin-Morrey Spaces and Oscillations
  ( 2.6.2023 , function spaces seminar Jena )
• Adaptive near-best Quarklet Tree Approximation
  ( 10.2.2023 , Rhein-Ruhr-Workshop , Bestwig )
• Quarklet Characterizations for Triebel-Lizorkin Spaces
  ( 6.10.2022 , International Conference on Function Spaces and Applications , Apolda )
• Adaptive near-best Quarklet Tree Approximation
  ( 1.8.2022 , Siegmundsburg seminar )
• B-Spline Quarklets and their Connections to the Theory of biorthogonal Multiwavelets
  ( 15.7.2022 , function spaces seminar Jena )
• Quarklets and their Connections to the Theory of biorthogonal Multiwavelets
  ( 6.7.2022 , Oberseminar zur Numerik und Optimierung Marburg )
• Poster: "Quarklet Characterizations for Triebel-Lizorkin spaces"
  ( 23.6.2022 , Conference "Applied Harmonic Analysis and Friends", Strobl, Austria )
• Triebel-Lizorkin-Morrey Spaces and Differences: Characterizations and Applications
  ( 3.3.2022 , Ruhr-Universität Bochum, Research Seminar Numerical Analysis )
• Quarklet Characterizations for Triebel-Lizorkin Spaces
  ( 2.2.2022 , Oberseminar zur Numerik und Optimierung Marburg )
• Quarklet Characterizations for Triebel-Lizorkin Spaces
  ( 31.8.2021 , Siegmundsburg seminar )
• Quarklet Characterizations for Triebel-Lizorkin and Triebel-Lizorkin-Morrey Spaces
  ( 2.7.2021 , function spaces seminar Jena )
• Quarklet Characterizations for Triebel-Lizorkin Spaces
  ( 16.6.2021 , Oberseminar zur Numerik und Optimierung Marburg )
• Triebel-Lizorkin-Morrey spaces and differences: characterizations and applications
  ( 16.12.2020 , Oberseminar zur Numerik und Optimierung Marburg )
• Truncation in Besov-Morrey and Triebel-Lizorkin-Morrey spaces
  ( 10.7.2020 , function spaces seminar Jena )
• Besov-Morrey spaces and truncations - an introduction
  ( 12.2.2020 , function spaces seminar Jena )
• Besov-Morrey spaces and differences
  ( 27.1.2020 , PhD seminar Jena )
• Besov-Morrey spaces and differences
  ( 26.8.2019 , Siegmundsburg seminar )
• Triebel-Lizorkin-Morrey spaces and differences
  ( 14.6.2019 , FSDONA, Turku, Finnland )
• Triebel-Lizorkin-Morrey spaces and differences: necessary conditions
  ( 18.1.2019 , function spaces seminar Jena )
• Triebel-Lizorkin-Morrey spaces and differences: sufficient conditions
  ( 11.1.2019 , function spaces seminar Jena )
• Triebel-Lizorkin-Morrey spaces and differences
  ( 23.11.2018 , The Prague seminar on function spaces )
• Strichartz-Charakterisierungen von F^{s}_{p,q}
  ( 24.7.2018 , Siegmundsburg seminar )
• Characterizations of Triebel-Lizorkin spaces by differences
  ( 14.5.2018 , PhD seminar Jena )

Short CV:

• since 9/2023 : Principal Investigator at the Philipps-Universität Marburg
  (Workgroup Numerics, DFG project "Adaptive Quarklet Methods for the numerical Solution of Elliptic Partial Differential Equations with exponential Convergence")
• 6/2021 - 5/2023 : Postdoc at the Philipps-Universität Marburg
  (Workgroup Numerics, DFG project "adaptive high-order quarklet frame methods for elliptic operator equations")
• 3/2018 - 5/2021 : Dr. rer. nat. in Mathematics at the Friedrich-Schiller-University Jena
  ( summa cum laude )
• 2015 - 2017 : M. Sc. in Mathematics at the Friedrich-Schiller-University Jena
  (final mark : 1,0 ) (Examenspreis of the dean of the department of mathematics and computer science)
• 2012 - 2015 : B. Sc. in Mathematics at the Friedrich-Schiller-University Jena
  
• 2002 - 2010 : Abitur at the Friedrich-Schiller-Gymnasium Eisenberg
  (final mark : 1,0)
• 22.06.1991 : born in Speyer (Germany)
  

Teaching (past semesters, Jena and Marburg)

• Lecture Nonlinear Optimization
  (M.Sc. Mathematik , summer term 2023)
• Exercise Analysis 2
  (B.Sc. Mathematik , summer term 2020)
• Exercise Analysis 1
  (B.Sc. Mathematik , winter term 2019/2020)
• Exercise Numerische Mathematik
  (B.Sc. Informatik , summer term 2019)
• Exercise Mathematik 1
  (B.Sc. Werkstoffwissenschaften , winter term 2018/2019)
• Exercise Analysis 2
  (Lehramt Gymnasium , summer term 2018)
• Exercise Mathematik 1
  (B.Sc. Werkstoffwissenschaften , winter term 2017/2018)
• Exercise Analysis 1
  (Lehramt Gymnasium , winter term 2017/2018)
• Tutorial Numerische Mathematik
  (B.Sc. Informatik , summer term 2017)

Some Links

Forschungsgruppe Funktionenräume Jena
Prof. Sickel (Jena)