| Abstract: | A constructive analytic function f is defined as a pair of form (A, ), where. A is a fundamental sequence in some constructive metric space and 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.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 50, pp. 49–58, 1976. Result announced November 1, 1973.The author thanks N. A. Shanin, who suggested the consideration of the approximative approach to the definition of a constructive analytic function. |
