Effective properties of sets and functions in metric spaces with computability structure
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
On the computability of Walsh functions
Theoretical Computer Science
Some Properties of the Effective Uniform Topological Space
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Integral of Fine Computable functions and Walsh Fourier series
Electronic Notes in Theoretical Computer Science (ENTCS)
Sequential Computability of a Function: Diagonal Space and Limiting Recursion
Electronic Notes in Theoretical Computer Science (ENTCS)
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We propose a sequential-based definition of locally uniformly Fine-computable functions together with a definition of effective locally uniform convergence. This definition of computability makes some discontinuous functions, which may diverge, computable. It is proved that a locally uniformly Fine-computable function can be approximated effectively locally uniformly by a Fine-computable sequence of binary step functions on the unit interval [0; 1) with respect to the Fine metric. We also introduce effective integrability for locally uniformly Fine-computable functions, and prove that Walsh-Fourier coeffcients of an effectively integrable function f form a computable sequence of reals. It is also proved that S2n f, where Snf is the partial sum of the Walsh-Fourier series, Fine-converges effectively locally uniformly to f.