Strict s-Numbers of Non-compact Sobolev Embeddings into Continuous Functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10408296" target="_blank" >RIV/00216208:11320/19:10408296 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=e5qugIUEh2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=e5qugIUEh2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00365-018-9448-0" target="_blank" >10.1007/s00365-018-9448-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Strict s-Numbers of Non-compact Sobolev Embeddings into Continuous Functions

Popis výsledku v původním jazyce

For limiting noncompact Sobolev embeddings into continuous functions, we study the behavior of approximation, Gelfand, Kolmogorov, Bernstein and isomorphism s-numbers. In the one-dimensional case, the exact values of the above-mentioned strict s-numbers are obtained, and in the higher dimensions sharp estimates for asymptotic behavior of the strict s-numbers are established. As all known results for s-numbers of Sobolev type embeddings are studied mainly under the compactness assumption, our work is an extension of existing results and reveal an interesting behavior of s-numbers in the limiting case when some of them (approximation, Gelfand, and Kolmogorov) have positive lower bound and others (Bernstein and isomorphism) are decreasing to zero. It also follows from our results that such limiting noncompact Sobolev embeddings are finitely strictly singular maps.

Název v anglickém jazyce

Strict s-Numbers of Non-compact Sobolev Embeddings into Continuous Functions

Popis výsledku anglicky

For limiting noncompact Sobolev embeddings into continuous functions, we study the behavior of approximation, Gelfand, Kolmogorov, Bernstein and isomorphism s-numbers. In the one-dimensional case, the exact values of the above-mentioned strict s-numbers are obtained, and in the higher dimensions sharp estimates for asymptotic behavior of the strict s-numbers are established. As all known results for s-numbers of Sobolev type embeddings are studied mainly under the compactness assumption, our work is an extension of existing results and reveal an interesting behavior of s-numbers in the limiting case when some of them (approximation, Gelfand, and Kolmogorov) have positive lower bound and others (Bernstein and isomorphism) are decreasing to zero. It also follows from our results that such limiting noncompact Sobolev embeddings are finitely strictly singular maps.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA13-14743S" target="_blank" >GA13-14743S: Prostory funkcí, váhové nerovnosti a interpolace II</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Constructive Approximation

ISSN

0176-4276

e-ISSN

—

Svazek periodika

50

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

271-291

Kód UT WoS článku

000483710900003

EID výsledku v databázi Scopus

2-s2.0-85053466309