Miek Messerschmidt
About
I am currently employed as senior lecturer at the University of Pretoria. My current research centers around computational geometry and functional analysis.
Previously I held a Claude Leon postdoctoral fellowship at the University of Pretoria (2016-2017) and a postdoctoral fellowship at the North-west University (2014-2016).
I completed my PhD at Leiden University in November of 2013 under supervision of Marcel de Jeu, with thesis titled Positive representations on ordered Banach spaces.
Contact
Email: miek(dot)messerschmidt(at)up(dot)ac(anotherdot)za
Office: University of Pretoria (Hatfield); Botany Building; Room 2-7.
[github] [ResearchGate] [arXiv] [MathOverflow] [linkedin] [orcid]
Publications
Eder Kikianty, Miek Messerschmidt, Luan Naude, Mark Roelands, Christopher Schwanke, Walt van Amstel, Jan Harm van der Walt, Marten Wortel. L-functional analysis
https://arxiv.org/abs/2403.10222Messerschmidt, M., Kikianty, E. On Compact Packings of Euclidean Space with Spheres of Finitely Many Sizes. Discrete Comput Geom (2024).
https://doi.org/10.1007/s00454-024-00628-y
http://arxiv.org/abs/2305.00758N.J. Laustsen, M. Messerschmidt, M. Wortel. A surjective summation operator with no Lipschitz right inverse. Proc. Amer. Math. Soc. 152 (2024), 253-266
https://doi.org/10.1090/proc/16496M. Messerschmidt. The number of configurations of radii that can occur in compact packings of the plane with discs of n sizes is finite. Discrete Comput Geom 71, 667–682 (2024).
https://doi.org/10.1007/s00454-022-00471-z
https://arxiv.org/abs/2110.15831S. ter Horst, M. Messerschmidt, A.C.M. Ran. Equivalence After Extension and Schur Coupling for Relatively Regular Operators. Integral Equations and Operator Theory 92, 40 (2020).
https://arxiv.org/abs/2005.14563
https://doi.org/10.1007/s00020-020-02597-2M. Messerschmidt. On compact packings of the plane with circles of three radii. Computational Geometry. Volume 86, January 2020, 101564.
https://doi.org/10.1016/j.comgeo.2019.05.002
https://arxiv.org/abs/1709.03487M. Messerschmidt. A family of quotient maps of $\ell^\infty$ that do not admit uniformly continuous right inverses (2019)
arxiv.org/abs/1909.10417M. Messerschmidt. A Pointwise Lipschitz Selection Theorem. Set-Valued and Variational Analysis. Volume 27, pp. 223-240(2019)
10.1007/s11228-017-0455-2
arxiv.org/abs/1611.08435S. ter Horst, M. Messerschmidt, A.C.M. Ran, M. Roelands. Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces. Bulletin London Mathematical Society Volume 51 (2019) 1005-1014
10.1112/blms.12292
arxiv.org/abs/1901.09254M. Messerschmidt. On the Lipschitz decomposition problem in ordered Banach spaces and its connections to other branches of mathematics. Positivity and Noncommutative Analysis (2019) Birkhauser. pp 405-423. Festschrift in honour of Ben de Pagter on the occasion of his 65th birthday.
https://doi.org/10.1007/978-3-030-10850-2 22M. Messerschmidt. Strong Klee-Andô Theorems through an Open Mapping Theorem for cone-valued multi-functions. Journal of Functional Analysis. Volume 275, Issue 12, 15 December 2018, Pages 3325-3337.
10.1016/j.jfa.2018.02.008
arxiv.org/abs/1606.00249S. ter Horst, M. Messerschmidt, A.C.M. Ran, M. Roelands, M. Wortel. Equivalence after extension and Schur coupling coincide for inessential operators. Indagationes Mathematicae (N.S.) 29 (2018), no. 5, 1350--1361.
10.1016/j.indag.2018.07.001
arxiv.org/abs/1706.09177M. Messerschmidt and M. Wortel. The intrinsic metric on the unit sphere of a normed space. 2015
arxiv.org/abs/1510.07442S. ter Horst, M. Messerschmidt, A. Ran. Equivalence after extension for compact operators on Banach spaces Journal of Mathematical Analysis and Applications. 431 (2015), pp. 136–149
doi:10.1016/j.jmaa.2015.05.059
arxiv.org/abs/1503.07350M. Messerschmidt. Geometric duality theory for cones in dual pairs of vector spaces. Journal of Functional Analysis. 269 (2015), pp. 2018-2044
doi:10.1016/j.jfa.2015.04.022
arxiv.org/abs/1407.2434M. Messerschmidt. Normality of spaces of operators and quasi-lattices. Positivity. 19 (2015), pp. 695-724
doi:10.1007/s11117-015-0323-y
arxiv.org/abs/1307.1415M. de Jeu, and M. Messerschmidt. A strong open mapping theorem for surjections from cones onto Banach spaces. Advances in Mathematics. 259 (2014) p.43-66
doi:10.1016/j.aim.2014.03.008
arxiv.org/abs/1302.2822M. de Jeu, M. Messerschmidt, and M. Wortel. Crossed products of Banach algebras. II.
arxiv.org/abs/1305.2304M. de Jeu, and M. Messerschmidt. Crossed products of Banach algebras. III.
arxiv.org/abs/1306.6290
