Computability
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Computability on the probability measures on the Borel sets of the unit interval
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Exact real number computations relative to hereditarily total functionals
Theoretical Computer Science
A Foundation for Computable Analysis
SOFSEM '97 Proceedings of the 24th Seminar on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Computing the solution of the Korteweg-de Vries equation with arbitrary precision on turing machines
Theoretical Computer Science
Towards computability of elliptic boundary value problems in variational formulation
Journal of Complexity
Computing Schrödinger propagators on Type-2 Turing machines
Journal of Complexity
Computable Analysis of the Abstract Cauchy Problem in a Banach Space and Its Applications (I)
Electronic Notes in Theoretical Computer Science (ENTCS)
Revising Type-2 Computation and Degrees of Discontinuity
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Effectivity on Continuous Functions in Topological Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
On computably locally compact hausdorff spaces
Mathematical Structures in Computer Science
An Algorithm for Computing Fundamental Solutions
Electronic Notes in Theoretical Computer Science (ENTCS)
Computability on subsets of locally compact spaces
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
The role of algebraic models and type-2 theory of effectivity in special purpose processor design
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Computable analysis of a non-homogeneous boundary-value problem for the korteweg-de vries equation
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Computability and continuity on the real arithmetic hierarchy and the power of type-2 nondeterminism
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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The theory of generalized functions is the foundation of the modern theory of partial differential equations (PDE). As computers are playing an ever-larger role in solving PDEs, it is important to know those operations involving generalized functions in analysis and PDE that can be computed on digital computers. In this article, we introduce natural concepts of computability on test functions and generalized functions, as well as computability on Schwartz test functions and tempered distributions. Type-2 Turing machines are used as the machine model [Weihrauch 2000]. It is shown here that differentiation and integration on distributions are computable operators, and various types of Fourier transforms and convolutions are also computable operators. As an application, it is shown that the solution operator of the distributional inhomogeneous three dimensional wave equation is computable.