Problems of approximation theory in abstract linear spaces

2021/04/09 by A. S. Serdyuk, Serdyuk, Anatolii S., Andrii Shidlich +1
Mathematics · #41A17 #41A29 #41A46 #41A65 #42A10 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2104.04252

openalex publication_date 2021/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This review paper presents the results, which cover the study of current problems of approximation theory in abstract linear spaces. Such research has been actively developed since the 2000s, based on the ideas and approaches initiated in the articles by Stepanets. In particular, the review contains results concerning the best, best n-term approximations and widths of some functional compacts in the spaces \mathcal S^p. Direct and inverse approximation theorems are also formulated in these spaces.

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