Adaptive Fourier decomposition in Hp
In this paper, we study decomposition of functions in Hardy spaces Hp(T)(1
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2019-04, Vol.42 (6), p.2016-2024 |
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| container_end_page | 2024 |
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| container_issue | 6 |
| container_start_page | 2016 |
| container_title | Mathematical methods in the applied sciences |
| container_volume | 42 |
| creator | Wang, Yanbo Qian, Tao |
| description | In this paper, we study decomposition of functions in Hardy spaces
Hp(T)(1 |
| doi_str_mv | 10.1002/mma.5494 |
| format | Article |
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Hp(T)(1<p<∞). First, we will give a direct application of adaptive Fourier decomposition (AFD) of
H2(T) to functions in
Hp(T). Then, we study adaptive decomposition by the system
1
D:=ea(z)=Aa,p1−āz,a∈D,
where Aa,p is the normalization factor making ea(z) to be of unit p‐norm. Under the proposed decomposition procedure, we show that every
f∈Hp(T) can be effectively expressed by a linear combination of
{ean(z)}n=1+∞. We give a maximal selection principle of
ean at the nth step and prove the convergence.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.5494</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>adaptive fourier decomposition ; Adaptive systems ; Decomposition ; Hardy space ; supporting functional ; Szegö kernel</subject><ispartof>Mathematical methods in the applied sciences, 2019-04, Vol.42 (6), p.2016-2024</ispartof><rights>2019 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0003-4754-207X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.5494$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.5494$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,777,781,1412,27905,27906,45555,45556</link.rule.ids></links><search><creatorcontrib>Wang, Yanbo</creatorcontrib><creatorcontrib>Qian, Tao</creatorcontrib><title>Adaptive Fourier decomposition in Hp</title><title>Mathematical methods in the applied sciences</title><description>In this paper, we study decomposition of functions in Hardy spaces
Hp(T)(1<p<∞). First, we will give a direct application of adaptive Fourier decomposition (AFD) of
H2(T) to functions in
Hp(T). Then, we study adaptive decomposition by the system
1
D:=ea(z)=Aa,p1−āz,a∈D,
where Aa,p is the normalization factor making ea(z) to be of unit p‐norm. Under the proposed decomposition procedure, we show that every
f∈Hp(T) can be effectively expressed by a linear combination of
{ean(z)}n=1+∞. We give a maximal selection principle of
ean at the nth step and prove the convergence.</description><subject>adaptive fourier decomposition</subject><subject>Adaptive systems</subject><subject>Decomposition</subject><subject>Hardy space</subject><subject>supporting functional</subject><subject>Szegö kernel</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNotkF1LwzAYhYMoWKfgTyjobeb75qNpLstwm7DhzXYdMpNAxtrGtlP2722ZV8_N4ZzDQ8gzwhwB2Ftd27kUWtyQDEFrikIVtyQDVEAFQ3FPHvr-CAAlIsvIa-VsGuKPz5ftuYu-y53_auvU9nGIbZPHJl-nR3IX7Kn3T_-ckf3yfbdY083n6mNRbWhCXgjKQ-G0kAjcllyhPATpnQ48WKdVcMCVZ1JyC0FLXXpwHDTjwgUhQXp54DPycu1NXft99v1gjuOpZpw0DHUptBoxpug19RtP_mJSF2vbXQyCmQSYUYCZBJjttprI_wCW100y</recordid><startdate>201904</startdate><enddate>201904</enddate><creator>Wang, Yanbo</creator><creator>Qian, Tao</creator><general>Wiley Subscription Services, Inc</general><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0003-4754-207X</orcidid></search><sort><creationdate>201904</creationdate><title>Adaptive Fourier decomposition in Hp</title><author>Wang, Yanbo ; Qian, Tao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1364-3f6d945103a83715bf5ed9f3fad97fd037e2553a0f9598e0d309234df4505e5b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>adaptive fourier decomposition</topic><topic>Adaptive systems</topic><topic>Decomposition</topic><topic>Hardy space</topic><topic>supporting functional</topic><topic>Szegö kernel</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Yanbo</creatorcontrib><creatorcontrib>Qian, Tao</creatorcontrib><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Yanbo</au><au>Qian, Tao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptive Fourier decomposition in Hp</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2019-04</date><risdate>2019</risdate><volume>42</volume><issue>6</issue><spage>2016</spage><epage>2024</epage><pages>2016-2024</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>In this paper, we study decomposition of functions in Hardy spaces
Hp(T)(1<p<∞). First, we will give a direct application of adaptive Fourier decomposition (AFD) of
H2(T) to functions in
Hp(T). Then, we study adaptive decomposition by the system
1
D:=ea(z)=Aa,p1−āz,a∈D,
where Aa,p is the normalization factor making ea(z) to be of unit p‐norm. Under the proposed decomposition procedure, we show that every
f∈Hp(T) can be effectively expressed by a linear combination of
{ean(z)}n=1+∞. We give a maximal selection principle of
ean at the nth step and prove the convergence.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.5494</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0003-4754-207X</orcidid></addata></record> |
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| ispartof | Mathematical methods in the applied sciences, 2019-04, Vol.42 (6), p.2016-2024 |
| issn | 0170-4214 1099-1476 |
| language | eng |
| recordid | cdi_proquest_journals_2198497219 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | adaptive fourier decomposition Adaptive systems Decomposition Hardy space supporting functional Szegö kernel |
| title | Adaptive Fourier decomposition in Hp |
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