Differential and Falsified Sampling Expansions
Differential and falsified sampling expansions ∑ k ∈ Z d c k φ ( M j x + k ) , where M is a matrix dilation, are studied. In the case of differential expansions, c k = L f ( M - j · ) ( - k ) , where L is an appropriate differential operator. For a large class of functions φ , the approximation orde...
Gespeichert in:
| Veröffentlicht in: | The Journal of fourier analysis and applications 2018-10, Vol.24 (5), p.1276-1305 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1305 |
|---|---|
| container_issue | 5 |
| container_start_page | 1276 |
| container_title | The Journal of fourier analysis and applications |
| container_volume | 24 |
| creator | Kolomoitsev, Yu Krivoshein, A. Skopina, M. |
| description | Differential and falsified sampling expansions
∑
k
∈
Z
d
c
k
φ
(
M
j
x
+
k
)
, where
M
is a matrix dilation, are studied. In the case of differential expansions,
c
k
=
L
f
(
M
-
j
·
)
(
-
k
)
, where
L
is an appropriate differential operator. For a large class of functions
φ
, the approximation order of differential expansions was recently studied. Some smoothness of the Fourier transform of
φ
from this class is required. In the present paper, we obtain similar results for a class of band-limited functions
φ
with the discontinuous Fourier transform. In the case of falsified expansions,
c
k
is the mathematical expectation of random integral average of a signal
f
near the point
M
-
j
k
. To estimate the approximation order of the falsified sampling expansions we compare them with the differential expansions. Error estimations in
L
p
-norm are given in terms of the Fourier transform of
f
. |
| doi_str_mv | 10.1007/s00041-017-9559-1 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_2110076044</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A718439922</galeid><sourcerecordid>A718439922</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-384ee34252436b34cf8dfcafa4e40a149acc5186887446c8daa6e9af37d38add3</originalsourceid><addsrcrecordid>eNp1kE9LAzEQxYMoWKsfwNuC562ZTbKbPZbaqlDwoJ7DmD8lZZtdky3otzdlBU-SQ4bM-73JPEJugS6A0uY-UUo5lBSashWiLeGMzEAwKIUUcJ5rWre5rttLcpXSntIKWMNmZPHgnbPRhtFjV2AwxQa75J23pnjFw9D5sCvWXwOG5PuQrsmFy31783vPyftm_bZ6Krcvj8-r5bbUTIixZJJby3glKs7qD8a1k8ZpdMgtpwi8Ra0FyFrKhvNaS4NY2xYdawyTaAybk7vJd4j959GmUe37Ywx5pKrgtHBNOc-qxaTaYWeVD64fI-p8jD143QfrfH5fNiA5a9uqygBMgI59StE6NUR_wPitgKqTrZpyVDlHdcpRQWaqiUlZG3Y2_n3lf-gHgI10Ag</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2110076044</pqid></control><display><type>article</type><title>Differential and Falsified Sampling Expansions</title><source>Springer Nature - Complete Springer Journals</source><creator>Kolomoitsev, Yu ; Krivoshein, A. ; Skopina, M.</creator><creatorcontrib>Kolomoitsev, Yu ; Krivoshein, A. ; Skopina, M.</creatorcontrib><description>Differential and falsified sampling expansions
∑
k
∈
Z
d
c
k
φ
(
M
j
x
+
k
)
, where
M
is a matrix dilation, are studied. In the case of differential expansions,
c
k
=
L
f
(
M
-
j
·
)
(
-
k
)
, where
L
is an appropriate differential operator. For a large class of functions
φ
, the approximation order of differential expansions was recently studied. Some smoothness of the Fourier transform of
φ
from this class is required. In the present paper, we obtain similar results for a class of band-limited functions
φ
with the discontinuous Fourier transform. In the case of falsified expansions,
c
k
is the mathematical expectation of random integral average of a signal
f
near the point
M
-
j
k
. To estimate the approximation order of the falsified sampling expansions we compare them with the differential expansions. Error estimations in
L
p
-norm are given in terms of the Fourier transform of
f
.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-017-9559-1</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Approximation ; Approximations and Expansions ; Differential equations ; Fourier Analysis ; Fourier transforms ; Mathematical analysis ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Matrix methods ; Operators (mathematics) ; Partial Differential Equations ; Sampling ; Signal,Image and Speech Processing ; Smoothness</subject><ispartof>The Journal of fourier analysis and applications, 2018-10, Vol.24 (5), p.1276-1305</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>COPYRIGHT 2018 Springer</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-384ee34252436b34cf8dfcafa4e40a149acc5186887446c8daa6e9af37d38add3</citedby><cites>FETCH-LOGICAL-c355t-384ee34252436b34cf8dfcafa4e40a149acc5186887446c8daa6e9af37d38add3</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/s00041-017-9559-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-017-9559-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27911,27912,41475,42544,51306</link.rule.ids></links><search><creatorcontrib>Kolomoitsev, Yu</creatorcontrib><creatorcontrib>Krivoshein, A.</creatorcontrib><creatorcontrib>Skopina, M.</creatorcontrib><title>Differential and Falsified Sampling Expansions</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>Differential and falsified sampling expansions
∑
k
∈
Z
d
c
k
φ
(
M
j
x
+
k
)
, where
M
is a matrix dilation, are studied. In the case of differential expansions,
c
k
=
L
f
(
M
-
j
·
)
(
-
k
)
, where
L
is an appropriate differential operator. For a large class of functions
φ
, the approximation order of differential expansions was recently studied. Some smoothness of the Fourier transform of
φ
from this class is required. In the present paper, we obtain similar results for a class of band-limited functions
φ
with the discontinuous Fourier transform. In the case of falsified expansions,
c
k
is the mathematical expectation of random integral average of a signal
f
near the point
M
-
j
k
. To estimate the approximation order of the falsified sampling expansions we compare them with the differential expansions. Error estimations in
L
p
-norm are given in terms of the Fourier transform of
f
.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximation</subject><subject>Approximations and Expansions</subject><subject>Differential equations</subject><subject>Fourier Analysis</subject><subject>Fourier transforms</subject><subject>Mathematical analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix methods</subject><subject>Operators (mathematics)</subject><subject>Partial Differential Equations</subject><subject>Sampling</subject><subject>Signal,Image and Speech Processing</subject><subject>Smoothness</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LAzEQxYMoWKsfwNuC562ZTbKbPZbaqlDwoJ7DmD8lZZtdky3otzdlBU-SQ4bM-73JPEJugS6A0uY-UUo5lBSashWiLeGMzEAwKIUUcJ5rWre5rttLcpXSntIKWMNmZPHgnbPRhtFjV2AwxQa75J23pnjFw9D5sCvWXwOG5PuQrsmFy31783vPyftm_bZ6Krcvj8-r5bbUTIixZJJby3glKs7qD8a1k8ZpdMgtpwi8Ra0FyFrKhvNaS4NY2xYdawyTaAybk7vJd4j959GmUe37Ywx5pKrgtHBNOc-qxaTaYWeVD64fI-p8jD143QfrfH5fNiA5a9uqygBMgI59StE6NUR_wPitgKqTrZpyVDlHdcpRQWaqiUlZG3Y2_n3lf-gHgI10Ag</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Kolomoitsev, Yu</creator><creator>Krivoshein, A.</creator><creator>Skopina, M.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20181001</creationdate><title>Differential and Falsified Sampling Expansions</title><author>Kolomoitsev, Yu ; Krivoshein, A. ; Skopina, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-384ee34252436b34cf8dfcafa4e40a149acc5186887446c8daa6e9af37d38add3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximation</topic><topic>Approximations and Expansions</topic><topic>Differential equations</topic><topic>Fourier Analysis</topic><topic>Fourier transforms</topic><topic>Mathematical analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix methods</topic><topic>Operators (mathematics)</topic><topic>Partial Differential Equations</topic><topic>Sampling</topic><topic>Signal,Image and Speech Processing</topic><topic>Smoothness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kolomoitsev, Yu</creatorcontrib><creatorcontrib>Krivoshein, A.</creatorcontrib><creatorcontrib>Skopina, M.</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>Kolomoitsev, Yu</au><au>Krivoshein, A.</au><au>Skopina, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Differential and Falsified Sampling Expansions</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2018-10-01</date><risdate>2018</risdate><volume>24</volume><issue>5</issue><spage>1276</spage><epage>1305</epage><pages>1276-1305</pages><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>Differential and falsified sampling expansions
∑
k
∈
Z
d
c
k
φ
(
M
j
x
+
k
)
, where
M
is a matrix dilation, are studied. In the case of differential expansions,
c
k
=
L
f
(
M
-
j
·
)
(
-
k
)
, where
L
is an appropriate differential operator. For a large class of functions
φ
, the approximation order of differential expansions was recently studied. Some smoothness of the Fourier transform of
φ
from this class is required. In the present paper, we obtain similar results for a class of band-limited functions
φ
with the discontinuous Fourier transform. In the case of falsified expansions,
c
k
is the mathematical expectation of random integral average of a signal
f
near the point
M
-
j
k
. To estimate the approximation order of the falsified sampling expansions we compare them with the differential expansions. Error estimations in
L
p
-norm are given in terms of the Fourier transform of
f
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-017-9559-1</doi><tpages>30</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1069-5869 |
| ispartof | The Journal of fourier analysis and applications, 2018-10, Vol.24 (5), p.1276-1305 |
| issn | 1069-5869 1531-5851 |
| language | eng |
| recordid | cdi_proquest_journals_2110076044 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Abstract Harmonic Analysis Approximation Approximations and Expansions Differential equations Fourier Analysis Fourier transforms Mathematical analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Matrix methods Operators (mathematics) Partial Differential Equations Sampling Signal,Image and Speech Processing Smoothness |
| title | Differential and Falsified Sampling Expansions |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-15T21%3A01%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Differential%20and%20Falsified%20Sampling%20Expansions&rft.jtitle=The%20Journal%20of%20fourier%20analysis%20and%20applications&rft.au=Kolomoitsev,%20Yu&rft.date=2018-10-01&rft.volume=24&rft.issue=5&rft.spage=1276&rft.epage=1305&rft.pages=1276-1305&rft.issn=1069-5869&rft.eissn=1531-5851&rft_id=info:doi/10.1007/s00041-017-9559-1&rft_dat=%3Cgale_proqu%3EA718439922%3C/gale_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2110076044&rft_id=info:pmid/&rft_galeid=A718439922&rfr_iscdi=true |