On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions
Let I = ( a , b ) × ( c , d ) ⊂ R + 2 be an index set and let { G α ( x ) } α ∈ I be a collection of Gaussian functions, i.e. G α ( x ) = exp ( - α 1 x 1 2 - α 2 x 2 2 ) , where α = ( α 1 , α 2 ) ∈ I , x = ( x 1 , x 2 ) ∈ R 2 . We present a complete description of the uniformly discrete sets Λ ⊂ R 2...
Gespeichert in:
| Veröffentlicht in: | The Journal of fourier analysis and applications 2022-06, Vol.28 (3), Article 55 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 3 |
| container_start_page | |
| container_title | The Journal of fourier analysis and applications |
| container_volume | 28 |
| creator | Zlotnikov, Ilya |
| description | Let
I
=
(
a
,
b
)
×
(
c
,
d
)
⊂
R
+
2
be an index set and let
{
G
α
(
x
)
}
α
∈
I
be a collection of Gaussian functions, i.e.
G
α
(
x
)
=
exp
(
-
α
1
x
1
2
-
α
2
x
2
2
)
, where
α
=
(
α
1
,
α
2
)
∈
I
,
x
=
(
x
1
,
x
2
)
∈
R
2
. We present a complete description of the uniformly discrete sets
Λ
⊂
R
2
such that every bandlimited signal
f
admits a stable reconstruction from the samples
{
f
∗
G
α
(
λ
)
}
λ
∈
Λ
. |
| doi_str_mv | 10.1007/s00041-022-09948-0 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_2675235624</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A706798733</galeid><sourcerecordid>A706798733</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2240-f27f5b8fbe583d8967f43371e0f0b2786d3b3a76288b87394f5749ed4a6e7e243</originalsourceid><addsrcrecordid>eNp9kF9LwzAUxYsoOKdfwKeAz503SZukj3O4-WcwYfoc0jaZGW1akw7x2xtXwTe5D_dyOb97LidJrjHMMAC_DQCQ4RQISaEoMpHCSTLBOcVpLnJ8GmdgRZxZcZ5chLAHIJhyOkmeNg69NMopj7aq7RvrdujTDu9opQ4hWOXQs_ZON8g6tO1VpQPqDLpTrm5sawddo-XBVYPtXLhMzoxqgr767dPkbXn_unhI15vV42K-TitCMkgN4SYvhSl1LmgtCsZNRinHGgyUhAtW05IqzogQpeC0yEzOs0LXmWKaa5LRaXIz3u1993HQYZD77uBdtJSE8ZzQnB1Vs1G1U42W1plu8KqKVevWVp3Txsb9nAPjRbShESAjUPkuBK-N7L1tlf-SGORPyHIMWcaQ5TFkCRGiIxSi2O20__vlH-obs6N9IQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2675235624</pqid></control><display><type>article</type><title>On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions</title><source>Springer Nature - Complete Springer Journals</source><creator>Zlotnikov, Ilya</creator><creatorcontrib>Zlotnikov, Ilya</creatorcontrib><description>Let
I
=
(
a
,
b
)
×
(
c
,
d
)
⊂
R
+
2
be an index set and let
{
G
α
(
x
)
}
α
∈
I
be a collection of Gaussian functions, i.e.
G
α
(
x
)
=
exp
(
-
α
1
x
1
2
-
α
2
x
2
2
)
, where
α
=
(
α
1
,
α
2
)
∈
I
,
x
=
(
x
1
,
x
2
)
∈
R
2
. We present a complete description of the uniformly discrete sets
Λ
⊂
R
2
such that every bandlimited signal
f
admits a stable reconstruction from the samples
{
f
∗
G
α
(
λ
)
}
λ
∈
Λ
.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-022-09948-0</identifier><language>eng</language><publisher>New York: Springer US</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, 2022-06, Vol.28 (3), Article 55</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022</rights><rights>COPYRIGHT 2022 Springer</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2240-f27f5b8fbe583d8967f43371e0f0b2786d3b3a76288b87394f5749ed4a6e7e243</cites><orcidid>0000-0002-1162-4033</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00041-022-09948-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-022-09948-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Zlotnikov, Ilya</creatorcontrib><title>On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>Let
I
=
(
a
,
b
)
×
(
c
,
d
)
⊂
R
+
2
be an index set and let
{
G
α
(
x
)
}
α
∈
I
be a collection of Gaussian functions, i.e.
G
α
(
x
)
=
exp
(
-
α
1
x
1
2
-
α
2
x
2
2
)
, where
α
=
(
α
1
,
α
2
)
∈
I
,
x
=
(
x
1
,
x
2
)
∈
R
2
. We present a complete description of the uniformly discrete sets
Λ
⊂
R
2
such that every bandlimited signal
f
admits a stable reconstruction from the samples
{
f
∗
G
α
(
λ
)
}
λ
∈
Λ
.</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>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kF9LwzAUxYsoOKdfwKeAz503SZukj3O4-WcwYfoc0jaZGW1akw7x2xtXwTe5D_dyOb97LidJrjHMMAC_DQCQ4RQISaEoMpHCSTLBOcVpLnJ8GmdgRZxZcZ5chLAHIJhyOkmeNg69NMopj7aq7RvrdujTDu9opQ4hWOXQs_ZON8g6tO1VpQPqDLpTrm5sawddo-XBVYPtXLhMzoxqgr767dPkbXn_unhI15vV42K-TitCMkgN4SYvhSl1LmgtCsZNRinHGgyUhAtW05IqzogQpeC0yEzOs0LXmWKaa5LRaXIz3u1993HQYZD77uBdtJSE8ZzQnB1Vs1G1U42W1plu8KqKVevWVp3Txsb9nAPjRbShESAjUPkuBK-N7L1tlf-SGORPyHIMWcaQ5TFkCRGiIxSi2O20__vlH-obs6N9IQ</recordid><startdate>20220601</startdate><enddate>20220601</enddate><creator>Zlotnikov, Ilya</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-1162-4033</orcidid></search><sort><creationdate>20220601</creationdate><title>On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions</title><author>Zlotnikov, Ilya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2240-f27f5b8fbe583d8967f43371e0f0b2786d3b3a76288b87394f5749ed4a6e7e243</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</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>Zlotnikov, Ilya</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>Zlotnikov, Ilya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2022-06-01</date><risdate>2022</risdate><volume>28</volume><issue>3</issue><artnum>55</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>Let
I
=
(
a
,
b
)
×
(
c
,
d
)
⊂
R
+
2
be an index set and let
{
G
α
(
x
)
}
α
∈
I
be a collection of Gaussian functions, i.e.
G
α
(
x
)
=
exp
(
-
α
1
x
1
2
-
α
2
x
2
2
)
, where
α
=
(
α
1
,
α
2
)
∈
I
,
x
=
(
x
1
,
x
2
)
∈
R
2
. We present a complete description of the uniformly discrete sets
Λ
⊂
R
2
such that every bandlimited signal
f
admits a stable reconstruction from the samples
{
f
∗
G
α
(
λ
)
}
λ
∈
Λ
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-022-09948-0</doi><orcidid>https://orcid.org/0000-0002-1162-4033</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1069-5869 |
| ispartof | The Journal of fourier analysis and applications, 2022-06, Vol.28 (3), Article 55 |
| issn | 1069-5869 1531-5851 |
| language | eng |
| recordid | cdi_proquest_journals_2675235624 |
| source | Springer Nature - Complete Springer 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 | On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T04%3A56%3A17IST&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=On%20Planar%20Sampling%20with%20Gaussian%20Kernel%20in%20Spaces%20of%20Bandlimited%20Functions&rft.jtitle=The%20Journal%20of%20fourier%20analysis%20and%20applications&rft.au=Zlotnikov,%20Ilya&rft.date=2022-06-01&rft.volume=28&rft.issue=3&rft.artnum=55&rft.issn=1069-5869&rft.eissn=1531-5851&rft_id=info:doi/10.1007/s00041-022-09948-0&rft_dat=%3Cgale_proqu%3EA706798733%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=2675235624&rft_id=info:pmid/&rft_galeid=A706798733&rfr_iscdi=true |