Tel: +2712 420-2819
Fax: +2712 420-3893
E-mail: [email protected]
Office: Vetman Building 1-15

Position: Associate Professor
Academic qualifications:  MSc, PhD(Pret)
NRF rating: C2

Open Access version of articles

Research Interests: Nonlinear PDE's and nonlinear theories of generalized functions; convergence spaces and applications; analysis of real and interval-valued functions; vector lattices and ordered linear topological spaces; non-Archimedean mathematics
Fields of Interest:  Functional analysis, general topology, applied mathematics

Publications over the past five years:

Journal articles 

de Jeu M, van der Walt JH, The order bidual of C(X) for a realcompact space. To appear in Quaestiones Mathematicae

O' Brien M, Troitsky V, Van der Walt JH, Net convergence structures with applications to vector lattices. To appear in Quaestiones Mathematicae

Agbebaku DF and van der Walt JH Differential chain of Algebras of Generalized Functions. To appear in Novi Sad Journal of Mathematics

Van der Walt JH  Convergence of sequences of semi-continuous functions.  Journal of Mathematical Analysis and Applications, 388(2012), 739-752

Van der Walt JH  The order completion method for system of nonlinear PDEs: Solutions of initial value problems.  Abstract and Applied Analysis, (2013), Article ID 739462, 12 pages electronic article

Khrennikov A, Shelkovich V, Van der Walt JH  Measure-free viewpoint on p-adic and adelic wavelets.  p-Adic and Ultrametric Analysis and its Applications, 5(3)(2013), 204-217

Anguelov R, Van der Walt JH  Algebraic and topological structure of some spaces of set-valued maps.  Computers and Mathematics with Applications, 66(2013), 1643-1654

Khrennikov AY, Shelkovich VM, Van der Walt JH  Adelic multiresolution analysis construction of wavelet bases and pseudo-differential operators.  Journal of Fourier Analysis and Applications, 19(6)(2013), 1323-1358

Van der Walt JH  The linear space of Hausdorff continuous interval functions.  Biomath 2(2)(2013), Article ID 1311261, 6 pages

Van der Walt JH  Linear and quasi-linear spaces of set-valued maps.  Computers and Mathematics with Applications, 68(2014), 1006-1015

Van der Walt JH  A closed graph theorem for order bounded operators. Quaestiones Mathematicae 39(2)(2016),167-178

Van der Walt JH Vector-valued interval functions and the Dedekind completion of C(X,E),  Positivity 21(2017), 1143–1159

Agbebaku DF and van der Walt JH The Order Completion Method:  A differential-algebraic representation. Novi Sad Journal of Mathematics 1(2017), 17-46

Agbebaku DF and van der Walt JH Differential algebras of generalised functions with dense singularities. Quaestiones Mathematicae 41(2)(2018) 283–301

Van der Walt JH The universal completion of C(X) and unbounded order convergence. Journal of Mathematical Analysis and Applications 460(1)(2018) 76–97

De Jeu M, Van der Walt JH On order continuous duals of vector lattices of continuous functions. Journal of Mathematical Analysis and Applications 479(2019) 581–60

Agbebaku DF and van der Walt JH Differential chain of Algebras of Generalized Functions. To appear in Novi Sad Journal of Mathematics

Van der Walt JH Category measures, the dual of C(K)δ and hyper-Stonean spaces. Proceedings of the American Mathematical Society 149(11)(2021) 4841-4852

O' Brien M, Troitsky V, Van der Walt JH  Net convergence structures with applications to vector lattices. To appear in Quaestiones Mathematicae

Conference Proceedings

Anguelov R, Agbebaku D Van der Walt JH  Hausdorff continuous solutions of conservation laws.  In MD Todorov (editor), Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 151-158, ISBN: 978-0-7354-1099-2

Van der Walt JH  Applications of convergence spaces to Vector Lattice Theory.  In J Dydak,G Gruenhage, J Kennedy, P Minc, D Shakhmatov, P Szeptycki, M Tuncali (eds), Topology Proceedings, (Summer Conference on Topology and its Applications, New York, USA), 41(2013), Topology Proceedings, pp 311-331, ISSN: 0146-4124

Van der Walt JH The Riesz Space of Minimal Usco Maps. Ordered Structures and Applications Positivity VII (Zaanen Centennial Conference), Editors: de Jeu M, de Pagter B, van Gaans O, Veraar M. 22-26 July 2013, Leiden, the Netherlands. Birkauser (2016)481 - 502

Book Chapters

Van der Walt JH Proceedings of the conference Positivity X, 8 to 12 July 2019, Pretoria, South Africa. Published in Birkhauser's series of books Trends in Mathematics

Van der Walt JH Representations of the Dedekind completions of spaces of continuous functions, Positivity and Noncommutative Analysis Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday Editors: Buskes, G., de Jeu, M., Dodds, P., Schep, A., Sukochev, F., van Neerven, J., Wickstead, A. (Eds.).

Van der Walt JH Representations of the Dedekind Completions of Spaces of Continuous Functions Positivity and Noncommutative Analysis (2019) 563-581