General Fourier coefficients
It is well known that if f ∈ L 2 ( 0 , 1 ) is an arbitrary function ( f ( x ) ≁ 0 , x ∈ [ 0 , 1 ] ) then its Fourier coefficients with respect to general orthonormal systems (ONS) may belong only to ℓ 2 . Thus in the general case it is impossible to estimate these coefficients by moduli of continuit...
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| Veröffentlicht in: | Acta mathematica Hungarica 2019-06, Vol.158 (1), p.109-131 |
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| container_title | Acta mathematica Hungarica |
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| creator | Gogoladze, L. Tsagareishvili, V. |
| description | It is well known that if
f
∈
L
2
(
0
,
1
)
is an arbitrary function (
f
(
x
)
≁
0
,
x
∈
[
0
,
1
]
) then its Fourier coefficients with respect to general orthonormal systems (ONS) may belong only to
ℓ
2
. Thus in the general case it is impossible to estimate these coefficients by moduli of continuity or moduli of smoothness of the given functions.
In the present paper conditions are found which should be satisfied by ONS so that the coefficients of some classes of functions can be estimated by modulus of continuity or modulus of smoothness of these functions. |
| doi_str_mv | 10.1007/s10474-019-00911-y |
| format | Article |
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f
∈
L
2
(
0
,
1
)
is an arbitrary function (
f
(
x
)
≁
0
,
x
∈
[
0
,
1
]
) then its Fourier coefficients with respect to general orthonormal systems (ONS) may belong only to
ℓ
2
. Thus in the general case it is impossible to estimate these coefficients by moduli of continuity or moduli of smoothness of the given functions.
In the present paper conditions are found which should be satisfied by ONS so that the coefficients of some classes of functions can be estimated by modulus of continuity or modulus of smoothness of these functions.</description><identifier>ISSN: 0236-5294</identifier><identifier>EISSN: 1588-2632</identifier><identifier>DOI: 10.1007/s10474-019-00911-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Coefficients ; Mathematics ; Mathematics and Statistics ; Smoothness</subject><ispartof>Acta mathematica Hungarica, 2019-06, Vol.158 (1), p.109-131</ispartof><rights>Akadémiai Kiadó, Budapest, Hungary 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-51bde8dd1dce4c672266b88201c5e0e0b193b685f36ba4bcb5b4466a6a9155b03</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/s10474-019-00911-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10474-019-00911-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gogoladze, L.</creatorcontrib><creatorcontrib>Tsagareishvili, V.</creatorcontrib><title>General Fourier coefficients</title><title>Acta mathematica Hungarica</title><addtitle>Acta Math. Hungar</addtitle><description>It is well known that if
f
∈
L
2
(
0
,
1
)
is an arbitrary function (
f
(
x
)
≁
0
,
x
∈
[
0
,
1
]
) then its Fourier coefficients with respect to general orthonormal systems (ONS) may belong only to
ℓ
2
. Thus in the general case it is impossible to estimate these coefficients by moduli of continuity or moduli of smoothness of the given functions.
In the present paper conditions are found which should be satisfied by ONS so that the coefficients of some classes of functions can be estimated by modulus of continuity or modulus of smoothness of these functions.</description><subject>Coefficients</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Smoothness</subject><issn>0236-5294</issn><issn>1588-2632</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AQhhdRsFb_gHgoeF6dmf3I5ijFVqHgRc9LdjORlJrU3fTQf280gjdPc3ne9x0eIa4R7hCguM8IutASsJQAJaI8nogZGuckWUWnYgakrDRU6nNxkfMWAIwCPRM3a-44VbvFqj-kltMi9tw0bWy5G_KlOGuqXear3zsXb6vH1-WT3Lysn5cPGxmpgEEaDDW7usY6so62ILI2OEeA0TAwBCxVsM40yoZKhxhM0NraylYlGhNAzcXt1LtP_eeB8-C34zfdOOmJyBC4wtBI0UTF1OecuPH71H5U6egR_LcFP1nwowX_Y8Efx5CaQnmEu3dOf9X_pL4AATJeWQ</recordid><startdate>20190601</startdate><enddate>20190601</enddate><creator>Gogoladze, L.</creator><creator>Tsagareishvili, V.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190601</creationdate><title>General Fourier coefficients</title><author>Gogoladze, L. ; Tsagareishvili, V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-51bde8dd1dce4c672266b88201c5e0e0b193b685f36ba4bcb5b4466a6a9155b03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Coefficients</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Smoothness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gogoladze, L.</creatorcontrib><creatorcontrib>Tsagareishvili, V.</creatorcontrib><collection>CrossRef</collection><jtitle>Acta mathematica Hungarica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gogoladze, L.</au><au>Tsagareishvili, V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>General Fourier coefficients</atitle><jtitle>Acta mathematica Hungarica</jtitle><stitle>Acta Math. Hungar</stitle><date>2019-06-01</date><risdate>2019</risdate><volume>158</volume><issue>1</issue><spage>109</spage><epage>131</epage><pages>109-131</pages><issn>0236-5294</issn><eissn>1588-2632</eissn><abstract>It is well known that if
f
∈
L
2
(
0
,
1
)
is an arbitrary function (
f
(
x
)
≁
0
,
x
∈
[
0
,
1
]
) then its Fourier coefficients with respect to general orthonormal systems (ONS) may belong only to
ℓ
2
. Thus in the general case it is impossible to estimate these coefficients by moduli of continuity or moduli of smoothness of the given functions.
In the present paper conditions are found which should be satisfied by ONS so that the coefficients of some classes of functions can be estimated by modulus of continuity or modulus of smoothness of these functions.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10474-019-00911-y</doi><tpages>23</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0236-5294 |
| ispartof | Acta mathematica Hungarica, 2019-06, Vol.158 (1), p.109-131 |
| issn | 0236-5294 1588-2632 |
| language | eng |
| recordid | cdi_proquest_journals_2225208752 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Coefficients Mathematics Mathematics and Statistics Smoothness |
| title | General Fourier coefficients |
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