Note on a Result of Kerman and Weit II
Let G be a locally compact topological group, equipped with a fixed left Haar measure μ . We show that if f is a compactly supported real valued continuous function on G which has a unique maximum or a unique minimum at a point in G , then the space generated by the span of left translations of { f...
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2013-04, Vol.19 (2), p.251-255 |
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| container_title | The Journal of fourier analysis and applications |
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| creator | Ray, Swagato K. Sarkar, Rudra P. |
| description | Let
G
be a locally compact topological group, equipped with a fixed left Haar measure
μ
. We show that if
f
is a compactly supported real valued continuous function on
G
which has a unique maximum or a unique minimum at a point in
G
, then the space generated by the span of left translations of {
f
n
∣
n
=1,2,3,…} is dense in
L
p
(
G
,
μ
), 1≤
p |
| doi_str_mv | 10.1007/s00041-012-9247-0 |
| format | Article |
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G
be a locally compact topological group, equipped with a fixed left Haar measure
μ
. We show that if
f
is a compactly supported real valued continuous function on
G
which has a unique maximum or a unique minimum at a point in
G
, then the space generated by the span of left translations of {
f
n
∣
n
=1,2,3,…} is dense in
L
p
(
G
,
μ
), 1≤
p
<∞, in the space of continuous functions, continuous compactly supported functions and in the space of continuous functions vanishing at ∞. Similar results are true when the group
G
is substituted by
G
-spaces with compact isotropy group.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-012-9247-0</identifier><language>eng</language><publisher>Boston: SP Birkhäuser Verlag Boston</publisher><subject>Abstract Harmonic Analysis ; Approximations and Expansions ; Fourier Analysis ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Signal,Image and Speech Processing</subject><ispartof>The Journal of fourier analysis and applications, 2013-04, Vol.19 (2), p.251-255</ispartof><rights>Springer Science+Business Media New York 2012</rights><rights>COPYRIGHT 2013 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-4554d873ea193efe1cefb439fe4c122d272b743e0379b59ce8b2c65324c5eae03</citedby><cites>FETCH-LOGICAL-c327t-4554d873ea193efe1cefb439fe4c122d272b743e0379b59ce8b2c65324c5eae03</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/s00041-012-9247-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-012-9247-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Ray, Swagato K.</creatorcontrib><creatorcontrib>Sarkar, Rudra P.</creatorcontrib><title>Note on a Result of Kerman and Weit II</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>Let
G
be a locally compact topological group, equipped with a fixed left Haar measure
μ
. We show that if
f
is a compactly supported real valued continuous function on
G
which has a unique maximum or a unique minimum at a point in
G
, then the space generated by the span of left translations of {
f
n
∣
n
=1,2,3,…} is dense in
L
p
(
G
,
μ
), 1≤
p
<∞, in the space of continuous functions, continuous compactly supported functions and in the space of continuous functions vanishing at ∞. Similar results are true when the group
G
is substituted by
G
-spaces with compact isotropy group.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Fourier Analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Signal,Image and Speech Processing</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKs_wFtO3rZm8tFsjqX4USwKongM2eykbGk3kmwP_nuzrGeZw7y8zDPDvITcAlsAY_o-M8YkVAx4ZbjUFTsjM1ACKlUrOC-aLU3RS3NJrnLeM8ZBaDEjd69xQBp76ug75tNhoDHQF0xHV6y-pV_YDXSzuSYXwR0y3vz1Ofl8fPhYP1fbt6fNerWtvOB6qKRSsq21QAdGYEDwGBopTEDpgfOWa95oKZAJbRplPNYN90sluPQKXbHnZDHt3bkD2q4PcUjOl2rx2PnYY-iKv9JQS861kAWACfAp5pww2O_UHV36scDsmIydkrElGTsmY8cjfGJyme13mOw-nlJf_voH-gUvwGNB</recordid><startdate>20130401</startdate><enddate>20130401</enddate><creator>Ray, Swagato K.</creator><creator>Sarkar, Rudra P.</creator><general>SP Birkhäuser Verlag Boston</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20130401</creationdate><title>Note on a Result of Kerman and Weit II</title><author>Ray, Swagato K. ; Sarkar, Rudra P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-4554d873ea193efe1cefb439fe4c122d272b743e0379b59ce8b2c65324c5eae03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Fourier Analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Signal,Image and Speech Processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ray, Swagato K.</creatorcontrib><creatorcontrib>Sarkar, Rudra P.</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ray, Swagato K.</au><au>Sarkar, Rudra P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Note on a Result of Kerman and Weit II</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2013-04-01</date><risdate>2013</risdate><volume>19</volume><issue>2</issue><spage>251</spage><epage>255</epage><pages>251-255</pages><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>Let
G
be a locally compact topological group, equipped with a fixed left Haar measure
μ
. We show that if
f
is a compactly supported real valued continuous function on
G
which has a unique maximum or a unique minimum at a point in
G
, then the space generated by the span of left translations of {
f
n
∣
n
=1,2,3,…} is dense in
L
p
(
G
,
μ
), 1≤
p
<∞, in the space of continuous functions, continuous compactly supported functions and in the space of continuous functions vanishing at ∞. Similar results are true when the group
G
is substituted by
G
-spaces with compact isotropy group.</abstract><cop>Boston</cop><pub>SP Birkhäuser Verlag Boston</pub><doi>10.1007/s00041-012-9247-0</doi><tpages>5</tpages></addata></record> |
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| identifier | ISSN: 1069-5869 |
| ispartof | The Journal of fourier analysis and applications, 2013-04, Vol.19 (2), p.251-255 |
| issn | 1069-5869 1531-5851 |
| language | eng |
| recordid | cdi_gale_infotracacademiconefile_A718422734 |
| source | SpringerLink Journals |
| subjects | Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing |
| title | Note on a Result of Kerman and Weit II |
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