Andreas Debrouwere

Department of Mathematics
Ghent University

Publications

Preprints / Submitted articles

  • A. Debrouwere, J. Vindas, Topological properties of convolutor spaces via the short-time Fourier transform, preprint. [Preprint]

Published / Accepted articles

  1. A. Debrouwere, J. Vindas, On weighted inductive limits of spaces of ultradifferentiable functions and their duals, Math. Nachr., accepted. [Preprint]
  2. A. Debrouwere, J. Vindas, A projective description of generalized Gelfand-Shilov spaces of Roumieu type, Proceedings of the 11th ISAAC congress, accepted. [Preprint]
  3. A. Debrouwere, H. Vernaeve, J. Vindas, A non-linear theory of infrahyperfunctions, Kyoto J. Math., accepted. [Preprint]
  4. A. Debrouwere, H. Vernaeve, J. Vindas, Optimal embeddings of ultradistributions into differential algebras, Monatsh. Math., in press. [Preprint/Article]
  5. A. Debrouwere, J. Vindas, On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth , Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Math. RACSAM 112 (2018), 473-508. [Preprint/Article]
  6. A. Debrouwere, E. A. Nigsch, Sheaves of nonlinear generalized function spaces, New York J. Math. 23 (2017), 1751–1789. [Preprint/Article]
  7. A. Debrouwere, J. Vindas, Solution to the first Cousin problem for vector-valued quasianalytic functions, Ann. Mat. Pura Appl. 196 (2017), 1983-2003. [Preprint/Article]
  8. A. Debrouwere, Generalized function algebras containing spaces of periodic ultradistributions, in: Generalized Functions and Fourier Analysis, pp. 59-78, Oper. Theory Adv. Appl., Vol. 260, Springer, 2017. [Preprint/Article]
  9. A. Debrouwere, J. Vindas, Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type, J. Math. Anal. Appl. 438 (2016), 889-908. [Preprint/Article]

Ph.D thesis

  • A. Debrouwere, Contributions to the linear and non-lineary theory of ultradistributions, Dissertation, Ghent University, 2018. [pdf]

Research

I work on various topics in functional analysis. My main interests are:
  • Linear and non-linear generalized function spaces
  • Classes of smooth functions
  • Time-frequency analysis
  • Homological methods in functional analysis
See my research statement for a more detailed account.

Curriculum Vitae

Click here to download my CV.

Talks

  • Whitney's extension theorem. A survey.
    • Logic and Analysis seminar, Ghent University, 25 October 2017.
  • Solution to the first Cousin problem for vector-valued quasianalytic functions. [Slides]
    • Second Workshop on Functional Analysis and Operator Theory, Valencia, 19 September 2017.
    • International Conference on Generalised Functions, Dubrovnik, 9 September 2016.
    • Logic and Analysis seminar, Ghent University, 22 February 2016.
  • On weighted inductive limits of spaces of ultradifferentiable functions and their duals. [Slides]
    • Analysis Seminar, Trier University, 7 September 2017.
    • 11th ISAAC congress, Växjö, 17 August 2017.
  • On the non-triviality of Gelfand-Shilov spaces. [Slides]
    • Phd Seminar, Ghent University, 15 May 2017.
    • Logic and Analysis seminar, Ghent University, 7 October 2015.
  • Sequence space representations of test functions and distributions.
    • Logic and Analysis seminar, Ghent University, 26 April 2016.
  • Abstract moment problems and their applications. [Slides]
    • Logic and Analysis seminar, Ghent University, 12 October 2016.
    • Workshop and Conference: Wien-Innsbruck-Novi Sad-Gent (WING 2016), Innsbruck, 30 June 2016.
  • On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth. [Slides]
    • International Workshop on Generalized Functions and Pseudo-differential Operators (Part of the VI Congress of Mathematicians of Macedonia), Ohrid, 16 June 2016.
    • Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Logroño (La Rioja), 7 June 2016.
    • Logic and Analysis seminar, Ghent University, 2 March 2016.
  • Optimal embeddings of ultradistributions into differential algebras. [Slides]
    • 10th ISAAC congress, Macau, 7 August 2015.
    • University of Novi Sad, 7 May 2015.
  • Various ways of defining distributions. Duality method, axiomatic approach, and analytic representations.
    • Logic and Analysis seminar, Ghent University, 1 April 2014.
  • Discrete characterization of wave front sets.
    • Logic and Analysis seminar, Ghent University, 19 November 2014.