Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness
We study properties of generalized K -functionals and generalized moduli of smoothness in L p (ℝ) spaces with 1 ≤ p < ∞ as well as in the space C (ℝ) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalenc...
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| Veröffentlicht in: | Analysis mathematica (Budapest) 2019-03, Vol.45 (1), p.1-24 |
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| container_title | Analysis mathematica (Budapest) |
| container_volume | 45 |
| creator | Artamonov, S. Runovski, K. Schmeisser, H.-J. |
| description | We study properties of generalized
K
-functionals and generalized moduli of smoothness in
L
p
(ℝ) spaces with 1 ≤
p
< ∞ as well as in the space
C
(ℝ) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support, generalized
K
-functionals generated by homogeneous functions and generalized moduli of smoothness. Our approach covers classical approximation methods,
K
-functionals related to fractional derivatives and fractional moduli of smoothness. |
| doi_str_mv | 10.1007/s10476-018-0302-1 |
| format | Article |
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K
-functionals and generalized moduli of smoothness in
L
p
(ℝ) spaces with 1 ≤
p
< ∞ as well as in the space
C
(ℝ) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support, generalized
K
-functionals generated by homogeneous functions and generalized moduli of smoothness. Our approach covers classical approximation methods,
K
-functionals related to fractional derivatives and fractional moduli of smoothness.</description><identifier>ISSN: 0133-3852</identifier><identifier>EISSN: 1588-273X</identifier><identifier>DOI: 10.1007/s10476-018-0302-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Approximation ; Continuity (mathematics) ; Convolution ; Convolution integrals ; Functionals ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Smoothness</subject><ispartof>Analysis mathematica (Budapest), 2019-03, Vol.45 (1), p.1-24</ispartof><rights>Akadémiai Kiadó, Budapest 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-a25a613d6ff99d3dee0b7a3ba7db73e2b96b963efb3f9d8daaeab9c532fc4de53</citedby><cites>FETCH-LOGICAL-c316t-a25a613d6ff99d3dee0b7a3ba7db73e2b96b963efb3f9d8daaeab9c532fc4de53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10476-018-0302-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10476-018-0302-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Artamonov, S.</creatorcontrib><creatorcontrib>Runovski, K.</creatorcontrib><creatorcontrib>Schmeisser, H.-J.</creatorcontrib><title>Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness</title><title>Analysis mathematica (Budapest)</title><addtitle>Anal Math</addtitle><description>We study properties of generalized
K
-functionals and generalized moduli of smoothness in
L
p
(ℝ) spaces with 1 ≤
p
< ∞ as well as in the space
C
(ℝ) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support, generalized
K
-functionals generated by homogeneous functions and generalized moduli of smoothness. Our approach covers classical approximation methods,
K
-functionals related to fractional derivatives and fractional moduli of smoothness.</description><subject>Analysis</subject><subject>Approximation</subject><subject>Continuity (mathematics)</subject><subject>Convolution</subject><subject>Convolution integrals</subject><subject>Functionals</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Smoothness</subject><issn>0133-3852</issn><issn>1588-273X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wNuCV6OZTPfr2BZbxYoHFbyF7CbRLdtNTXah9debZRXxIAQCM887zDyEnAO7AsbSaw9skiaUQUYZMk7hgIwgzjLKU3w9JCMGiBSzmB-TE-_XjLE8yXBEzHS7dXZXbWRb2Saa7aOZbFRdbapWq2jRNWVf95fRUjfaybr6DOV7-tOQtY8C_6f7YFVXV5E10dPG2va90d6fkiMTWH32_Y_Jy-LmeX5LV4_Lu_l0RUuEpKWSxzIBVIkxea5Qac2KVGIhU1WkqHmRJ-GhNgWaXGVKSi2LvIyRm3KidIxjcjHMDUd9dNq3Ym07168pOITrGUA6CRQMVOms904bsXXBgNsLYKLXKQadIugUvU4BIcOHjA9s86bd7-T_Q18-E3py</recordid><startdate>20190301</startdate><enddate>20190301</enddate><creator>Artamonov, S.</creator><creator>Runovski, K.</creator><creator>Schmeisser, H.-J.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190301</creationdate><title>Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness</title><author>Artamonov, S. ; Runovski, K. ; Schmeisser, H.-J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-a25a613d6ff99d3dee0b7a3ba7db73e2b96b963efb3f9d8daaeab9c532fc4de53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analysis</topic><topic>Approximation</topic><topic>Continuity (mathematics)</topic><topic>Convolution</topic><topic>Convolution integrals</topic><topic>Functionals</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Smoothness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Artamonov, S.</creatorcontrib><creatorcontrib>Runovski, K.</creatorcontrib><creatorcontrib>Schmeisser, H.-J.</creatorcontrib><collection>CrossRef</collection><jtitle>Analysis mathematica (Budapest)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Artamonov, S.</au><au>Runovski, K.</au><au>Schmeisser, H.-J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness</atitle><jtitle>Analysis mathematica (Budapest)</jtitle><stitle>Anal Math</stitle><date>2019-03-01</date><risdate>2019</risdate><volume>45</volume><issue>1</issue><spage>1</spage><epage>24</epage><pages>1-24</pages><issn>0133-3852</issn><eissn>1588-273X</eissn><abstract>We study properties of generalized
K
-functionals and generalized moduli of smoothness in
L
p
(ℝ) spaces with 1 ≤
p
< ∞ as well as in the space
C
(ℝ) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support, generalized
K
-functionals generated by homogeneous functions and generalized moduli of smoothness. Our approach covers classical approximation methods,
K
-functionals related to fractional derivatives and fractional moduli of smoothness.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10476-018-0302-1</doi><tpages>24</tpages></addata></record> |
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| ispartof | Analysis mathematica (Budapest), 2019-03, Vol.45 (1), p.1-24 |
| issn | 0133-3852 1588-273X |
| language | eng |
| recordid | cdi_proquest_journals_2185201174 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Analysis Approximation Continuity (mathematics) Convolution Convolution integrals Functionals Mathematical analysis Mathematics Mathematics and Statistics Smoothness |
| title | Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness |
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