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A Complete Asymptotic Expansion for the Quasi-interpolants of Gauß–Weierstraß Operators
We derive the complete asymptotic expansion for the quasi-interpolants of Gauß–Weierstraß operators W n and their left quasi-interpolants W n r with explicit representation of the coefficients. The results apply to all locally integrable real functions f on R satisfying the growth condition f t = O...
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| Published in: | Mediterranean journal of mathematics 2018-08, Vol.15 (4), p.1-10, Article 156 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c2318-b984a3f13e9b1ea3cd29f13056c3ac9f89a8ec1c97cfd7908a20aab3af36da4c3 |
| container_end_page | 10 |
| container_issue | 4 |
| container_start_page | 1 |
| container_title | Mediterranean journal of mathematics |
| container_volume | 15 |
| creator | Abel, Ulrich Agratini, Octavian Păltănea, Radu |
| description | We derive the complete asymptotic expansion for the quasi-interpolants of Gauß–Weierstraß operators
W
n
and their left quasi-interpolants
W
n
r
with explicit representation of the coefficients. The results apply to all locally integrable real functions
f
on
R
satisfying the growth condition
f
t
=
O
e
c
t
2
as
t
→
+
∞
, for some
c
>
0
. All expansions are shown to be valid also for simultaneous approximation. |
| doi_str_mv | 10.1007/s00009-018-1195-8 |
| format | article |
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W
n
and their left quasi-interpolants
W
n
r
with explicit representation of the coefficients. The results apply to all locally integrable real functions
f
on
R
satisfying the growth condition
f
t
=
O
e
c
t
2
as
t
→
+
∞
, for some
c
>
0
. All expansions are shown to be valid also for simultaneous approximation.</description><identifier>ISSN: 1660-5446</identifier><identifier>EISSN: 1660-5454</identifier><identifier>DOI: 10.1007/s00009-018-1195-8</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Asymptotic methods ; Asymptotic series ; Mathematics ; Mathematics and Statistics ; Operators</subject><ispartof>Mediterranean journal of mathematics, 2018-08, Vol.15 (4), p.1-10, Article 156</ispartof><rights>Springer International Publishing AG, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2318-b984a3f13e9b1ea3cd29f13056c3ac9f89a8ec1c97cfd7908a20aab3af36da4c3</citedby><cites>FETCH-LOGICAL-c2318-b984a3f13e9b1ea3cd29f13056c3ac9f89a8ec1c97cfd7908a20aab3af36da4c3</cites><orcidid>0000-0002-2406-4274 ; 0000-0003-1889-4850</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Abel, Ulrich</creatorcontrib><creatorcontrib>Agratini, Octavian</creatorcontrib><creatorcontrib>Păltănea, Radu</creatorcontrib><title>A Complete Asymptotic Expansion for the Quasi-interpolants of Gauß–Weierstraß Operators</title><title>Mediterranean journal of mathematics</title><addtitle>Mediterr. J. Math</addtitle><description>We derive the complete asymptotic expansion for the quasi-interpolants of Gauß–Weierstraß operators
W
n
and their left quasi-interpolants
W
n
r
with explicit representation of the coefficients. The results apply to all locally integrable real functions
f
on
R
satisfying the growth condition
f
t
=
O
e
c
t
2
as
t
→
+
∞
, for some
c
>
0
. All expansions are shown to be valid also for simultaneous approximation.</description><subject>Asymptotic methods</subject><subject>Asymptotic series</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators</subject><issn>1660-5446</issn><issn>1660-5454</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM9KAzEQxoMoWKsP4C3gOZo_u9vNsZTaCoUiKB48hGma6JZ2syZZsDffwQfow_RNfBJTVvTkXGYGvu-b4YfQJaPXjNLBTaCpJKGsJIzJnJRHqMeKgpI8y7Pj3zkrTtFZCCtKuWSC99DzEI_cplmbaPAwbDdNdLHSePzeQB0qV2PrPI6vBt-3ECpS1dH4xq2hjgE7iyfQ7ndfH59PpjI-RA_7HZ43xkN0PpyjEwvrYC5-eh893o4fRlMym0_uRsMZ0VykfxeyzEBYJoxcMANCL7lMG80LLUBLW0oojWZaDrRdDiQtgVOAhQAriiVkWvTRVZfbePfWmhDVyrW-TicVTymccV6IpGKdSnsXgjdWNb7agN8qRtWBoeoYqsRQHRiqMnl45wlJW78Y_5f8v-kbsXl3ng</recordid><startdate>20180801</startdate><enddate>20180801</enddate><creator>Abel, Ulrich</creator><creator>Agratini, Octavian</creator><creator>Păltănea, Radu</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-2406-4274</orcidid><orcidid>https://orcid.org/0000-0003-1889-4850</orcidid></search><sort><creationdate>20180801</creationdate><title>A Complete Asymptotic Expansion for the Quasi-interpolants of Gauß–Weierstraß Operators</title><author>Abel, Ulrich ; Agratini, Octavian ; Păltănea, Radu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2318-b984a3f13e9b1ea3cd29f13056c3ac9f89a8ec1c97cfd7908a20aab3af36da4c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Asymptotic methods</topic><topic>Asymptotic series</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abel, Ulrich</creatorcontrib><creatorcontrib>Agratini, Octavian</creatorcontrib><creatorcontrib>Păltănea, Radu</creatorcontrib><collection>CrossRef</collection><jtitle>Mediterranean journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Abel, Ulrich</au><au>Agratini, Octavian</au><au>Păltănea, Radu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Complete Asymptotic Expansion for the Quasi-interpolants of Gauß–Weierstraß Operators</atitle><jtitle>Mediterranean journal of mathematics</jtitle><stitle>Mediterr. J. Math</stitle><date>2018-08-01</date><risdate>2018</risdate><volume>15</volume><issue>4</issue><spage>1</spage><epage>10</epage><pages>1-10</pages><artnum>156</artnum><issn>1660-5446</issn><eissn>1660-5454</eissn><abstract>We derive the complete asymptotic expansion for the quasi-interpolants of Gauß–Weierstraß operators
W
n
and their left quasi-interpolants
W
n
r
with explicit representation of the coefficients. The results apply to all locally integrable real functions
f
on
R
satisfying the growth condition
f
t
=
O
e
c
t
2
as
t
→
+
∞
, for some
c
>
0
. All expansions are shown to be valid also for simultaneous approximation.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00009-018-1195-8</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-2406-4274</orcidid><orcidid>https://orcid.org/0000-0003-1889-4850</orcidid></addata></record> |
| fulltext | fulltext |
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| ispartof | Mediterranean journal of mathematics, 2018-08, Vol.15 (4), p.1-10, Article 156 |
| issn | 1660-5446 1660-5454 |
| language | eng |
| recordid | cdi_proquest_journals_2056212263 |
| source | Springer Link |
| subjects | Asymptotic methods Asymptotic series Mathematics Mathematics and Statistics Operators |
| title | A Complete Asymptotic Expansion for the Quasi-interpolants of Gauß–Weierstraß Operators |
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