Let Tn be the linear Hadamard convolution operator acting over Hardy space Hq, 1≤q≤∞. We call Tn a best approximation-preserving operator (BAP operator) if Tn(en)=en, where en(z):=zn, and if ∥Tn(f)∥q≤En(f)q for all f∈Hq, where En(f)q is the best approximation by algebraic polynomials of degree a most n−1 in Hq space. We give necessary and sufficient conditions for Tn to be a BAP operator over H∞. We apply this result to establish an exact lower bound for the best approximation of bounded holomorphic functions. In particular, we show that the Landau-type inequality ∣∣fˆn∣∣+c∣∣fˆN∣∣≤En(f)∞, where c>0 and n
Keyword: best approximation; cauchy inequality; hadamard product; hardy space; landau inequality
Publication Name (dc.title) | Best approximation-preserving operators over Hardy space |
Author/s (dc.contributor.yazarlar) | F.G. Abdullayev, V.V. Savchuk, M.V. Savchuk |
Publication type (dc.type) | Makale |
Language (dc.language) | İngilizce |
Publication year (dc.date.issued) | 2023 |
National/International (dc.identifier.ulusaluluslararasi) | Uluslararası |
Source (dc.relation.journal) | Analysis and Mathematical Physics |
Number (dc.identifier.issue) | 4 |
Volume/Issue (dc.identifier.volume) | 13 |
Page (dc.identifier.startpage) | Article Number: 63 |
ISSN/ISBN (dc.identifier.issn) | ISSN: 1664-2368; Online ISSN: 1664-235X |
Publisher (dc.publisher) | Springer |
Databases (dc.contributor.veritaban) | Web of Science Core Collection |
Databases (dc.contributor.veritaban) | Springer |
Databases (dc.contributor.veritaban) | Scopus |
Index Type (dc.identifier.index) | SCI Expanded |
Index Type (dc.identifier.index) | Scopus |
Impact Factor (dc.identifier.etkifaktoru) | 1,7 / 2022-WOS / Son 5 yıl: 1,5 |
Abstract (dc.description.abstract) | Let Tn be the linear Hadamard convolution operator acting over Hardy space Hq, 1≤q≤∞. We call Tn a best approximation-preserving operator (BAP operator) if Tn(en)=en, where en(z):=zn, and if ∥Tn(f)∥q≤En(f)q for all f∈Hq, where En(f)q is the best approximation by algebraic polynomials of degree a most n−1 in Hq space. We give necessary and sufficient conditions for Tn to be a BAP operator over H∞. We apply this result to establish an exact lower bound for the best approximation of bounded holomorphic functions. In particular, we show that the Landau-type inequality ∣∣fˆn∣∣+c∣∣fˆN∣∣≤En(f)∞, where c>0 and n |
Abstract (dc.description.abstract) | Keyword: best approximation; cauchy inequality; hadamard product; hardy space; landau inequality |
URL (dc.rights) | https://link.springer.com/article/10.1007/s13324-023-00825-7 |
DOI (dc.identifier.doi) | 10.1007/s13324-023-00825-7 |
Faculty / Institute (dc.identifier.fakulte) | Fen Fakültesi |
Department (dc.identifier.bolum) | Uygulamalı Matematik ve Enformatik Bölümü |
Author(s) in the Institution (dc.contributor.author) | Fahreddin ABDULLAYEV |
Kayıt No (dc.identifier.kayitno) | BL3AB231F5 |
Record Add Date (dc.date.available) | 2023-07-24 |
Notes (Publication year) (dc.identifier.notyayinyili) | August 2023 |
Wos No (dc.identifier.wos) | WOS:001026546500001 |
Subject Headings (dc.subject) | best approximation |
Subject Headings (dc.subject) | cauchy inequality |
Subject Headings (dc.subject) | hadamard product |
Subject Headings (dc.subject) | hardy space |
Subject Headings (dc.subject) | landau inequality |