Year: 1965
Type: article
Abstract: Banach [1 introduced the concept of linear dimension into the theory of topological linear spaces.Extending the idea, Kolmogorov [2 defined the approximative dimension with a view to more definite comparison between dimensions of certain linear spaces..Besides the definition he gave some of its examples in the note [2.Among them we find a formula determining the approximative di- mension for the space A of regular analytic functions defined on a domain G of s complex variables, with which the comparison of dimensions for different s leads to a reasonable result.The proof is not given, only it is mentioned that the formula can be derived by the same method as is used for the evaluation of e-entropies.
Author: Isao Miyazaki
Institution: Saitama University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2068533250