On an approximative version of the notion of constructive analytic function
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 49-58
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A constructive analytic function f is defined as a pair of form $(A,\Omega)$, where $A$ is a fundamental sequence in some constructive metric space and $\Omega$ is a regulator of its convergence into itself. The pointwise-defined function $f$ corresponding to function $f^*$ turns out to be Bishop-differentiable [2], while the domain of $f^*$ is the limit of a growing sequence of compacta. The derivative of a constructive analytic function and the integral along a curve are defined approximatively. It is proved that the fundamental theorems of constructive complex analysis are valid for such functions. Eight items of literature are cited.
@article{ZNSL_1976_60_a4,
author = {E. Ya. Dantsin},
title = {On an approximative version of the notion of constructive analytic function},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {49--58},
publisher = {mathdoc},
volume = {60},
year = {1976},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a4/}
}
E. Ya. Dantsin. On an approximative version of the notion of constructive analytic function. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 49-58. http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a4/