Browsing Research Articles (Mathematics and Applied Mathematics) by UP Author "Van der Walt, Jan Harm"

Browsing Research Articles (Mathematics and Applied Mathematics) by UP Author "Van der Walt, Jan Harm"

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  • A closed graph theorem for order bounded operators 
    Van der Walt, Jan Harm (Routledge, 2016)
    The closed graph theorem is one of the cornerstones of linear functional analysis in Frechet spaces, and the extension of this result to more general topological vector spaces is a difficult problem comprising a great ...
  • Convergence of sequences of semi-continuous functions 
    Van der Walt, Jan Harm (Elsevier, 2012-04)
    In this paper we investigate how three well-known modes of convergence for (real-valued) functions are related to one another. In particular, we consider order convergence, pointwise convergence and continuous convergence ...
  • Limits of vector lattices 
    Van Amstel, Sarel Jakobus van der Walt; Van der Walt, Jan Harm (Elsevier, 2024-03)
    Please read abstract in the article.
  • The order completion method for systems of nonlinear PDEs: solutions of initial value problems 
    Van der Walt, Jan Harm; Stanek, Svatoslav (Hindawi Publishing Corporation, 2013)
    We present an existence result for generalized solutions of initial value problems obtained through the order completion method. The solutions we obtain satisfy the initial condition in a suitable extended sense, and each ...
  • Solutions of smooth nonlinear partial differential equations 
    Van der Walt, Jan Harm; Clark, Stephen (Hindawi Publishing Corporation, 2011-04-15)
    The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations PDEs . Recently, ...