Open AccessConvergence to boundary values in the topology of the inductive limit of generalized holder spaces
Author(s) -
Oleg Grober,
Tatyana A. Grober,
A. B. Bychkov
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/698/6/066025
Subject(s) - mathematics , limit (mathematics) , convergence (economics) , mathematical analysis , boundary (topology) , topology (electrical circuits) , modulus of continuity , class (philosophy) , direct limit , analytic function , boundary value problem , unit circle , uniform limit theorem , pure mathematics , computer science , type (biology) , combinatorics , ecology , artificial intelligence , economics , biology , economic growth
Both the functions theory of a complex variable and the approximation theory are often used in modern engineering sciences. In the present work, the spaces of analytic functions inside the unit circle satisfying on the boundary a strong Holder condition for a rather wide class of the modulus of continuity are considered. The convergence question of functions from these spaces to their boundary values in the topology of the inductive limit is studied.