Sharp $L_p$-error estimates for sampling operators
We study approximation properties of linear sampling operators in the spaces $L_p$ for $1\le p
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| creator | Kolomoitsev, Yurii Lomako, Tetiana |
| description | We study approximation properties of linear sampling operators in the spaces
$L_p$ for $1\le p |
| doi_str_mv | 10.48550/arxiv.2202.05034 |
| format | Article |
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$L_p$ for $1\le p<\infty$. By means of the Steklov averages, we introduce a new
measure of smoothness that simultaneously contains information on the
smoothness of a function in $L_p$ and discrete information on the behaviour of
a function at sampling points. The new measure of smoothness enables us to
improve and extend several classical results of approximation theory to the
case of linear sampling operators. In particular, we obtain matching direct and
inverse approximation inequalities for sampling operators in $L_p$, find the
exact order of decay of the corresponding $L_p$-errors for particular classes
of functions, and introduce a special $K$-functional and its realization
suitable for studying smoothness properties of sampling operators.</description><identifier>DOI: 10.48550/arxiv.2202.05034</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Classical Analysis and ODEs ; Mathematics - Numerical Analysis</subject><creationdate>2022-02</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2202.05034$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2202.05034$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kolomoitsev, Yurii</creatorcontrib><creatorcontrib>Lomako, Tetiana</creatorcontrib><title>Sharp $L_p$-error estimates for sampling operators</title><description>We study approximation properties of linear sampling operators in the spaces
$L_p$ for $1\le p<\infty$. By means of the Steklov averages, we introduce a new
measure of smoothness that simultaneously contains information on the
smoothness of a function in $L_p$ and discrete information on the behaviour of
a function at sampling points. The new measure of smoothness enables us to
improve and extend several classical results of approximation theory to the
case of linear sampling operators. In particular, we obtain matching direct and
inverse approximation inequalities for sampling operators in $L_p$, find the
exact order of decay of the corresponding $L_p$-errors for particular classes
of functions, and introduce a special $K$-functional and its realization
suitable for studying smoothness properties of sampling operators.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Classical Analysis and ODEs</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzj1PwzAQxnEvDKjwAZjI0DXhfD476Ygq3qRIHegeXd0zRGqJdY4QfHtKYXr0Xx79jLmx0FDnPdyxfo2fDSJgAx4cXRp8fWfN1bIf8rIW1UkrKfN45FlKlU5V-JgP48dbNWVRnictV-Yi8aHI9f8uzPbxYbt-rvvN08v6vq85tFSviDpIvqO4CpFa31r0KVjcoSSE6EEig9vHdkd7Sy4Fkg4lCBNQism6hbn9uz2jh6wnlH4Pv_jhjHc_ZsA-Ew</recordid><startdate>20220210</startdate><enddate>20220210</enddate><creator>Kolomoitsev, Yurii</creator><creator>Lomako, Tetiana</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220210</creationdate><title>Sharp $L_p$-error estimates for sampling operators</title><author>Kolomoitsev, Yurii ; Lomako, Tetiana</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-94480f584c96c4757125f612b2ef20c50eca03dc7b4d143f64e82e6ea404fcf13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Classical Analysis and ODEs</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Kolomoitsev, Yurii</creatorcontrib><creatorcontrib>Lomako, Tetiana</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kolomoitsev, Yurii</au><au>Lomako, Tetiana</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sharp $L_p$-error estimates for sampling operators</atitle><date>2022-02-10</date><risdate>2022</risdate><abstract>We study approximation properties of linear sampling operators in the spaces
$L_p$ for $1\le p<\infty$. By means of the Steklov averages, we introduce a new
measure of smoothness that simultaneously contains information on the
smoothness of a function in $L_p$ and discrete information on the behaviour of
a function at sampling points. The new measure of smoothness enables us to
improve and extend several classical results of approximation theory to the
case of linear sampling operators. In particular, we obtain matching direct and
inverse approximation inequalities for sampling operators in $L_p$, find the
exact order of decay of the corresponding $L_p$-errors for particular classes
of functions, and introduce a special $K$-functional and its realization
suitable for studying smoothness properties of sampling operators.</abstract><doi>10.48550/arxiv.2202.05034</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Classical Analysis and ODEs Mathematics - Numerical Analysis |
| title | Sharp $L_p$-error estimates for sampling operators |
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