Riesz Bases of Reproducing Kernels in Small Fock Spaces
We give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock spaces F φ 2 , the spaces of entire functions f such that f e - φ ∈ L 2 ( C ) , where φ ( z ) = ( log + | z | ) β + 1 , 0 < β ≤ 1 . The first results in this direction are due to Borichev–Lyubar...
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| creator | Kellay, K. Omari, Y. |
| description | We give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock spaces
F
φ
2
, the spaces of entire functions
f
such that
f
e
-
φ
∈
L
2
(
C
)
, where
φ
(
z
)
=
(
log
+
|
z
|
)
β
+
1
,
0
<
β
≤
1
. The first results in this direction are due to Borichev–Lyubarskii who showed that
φ
with
β
=
1
is the largest weight for which the corresponding Fock space admits Riesz bases of reproducing kernels. Later, such bases were characterized by Baranov et al. in the case when
β
=
1
. The present paper answers a question in Baranov et al. by extending their results for all parameters
β
∈
(
0
,
1
)
. Our results are analogous to those obtained for the case
β
=
1
and those proved for Riesz bases of complex exponentials for the Paley–Wiener spaces. We also obtain a description of complete interpolating sequences in small Fock spaces with corresponding uniform norm. |
| doi_str_mv | 10.1007/s00041-019-09719-4 |
| format | Article |
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F
φ
2
, the spaces of entire functions
f
such that
f
e
-
φ
∈
L
2
(
C
)
, where
φ
(
z
)
=
(
log
+
|
z
|
)
β
+
1
,
0
<
β
≤
1
. The first results in this direction are due to Borichev–Lyubarskii who showed that
φ
with
β
=
1
is the largest weight for which the corresponding Fock space admits Riesz bases of reproducing kernels. Later, such bases were characterized by Baranov et al. in the case when
β
=
1
. The present paper answers a question in Baranov et al. by extending their results for all parameters
β
∈
(
0
,
1
)
. Our results are analogous to those obtained for the case
β
=
1
and those proved for Riesz bases of complex exponentials for the Paley–Wiener spaces. We also obtain a description of complete interpolating sequences in small Fock spaces with corresponding uniform norm.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-019-09719-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Approximations and Expansions ; Classical Analysis and ODEs ; Complex Variables ; Entire functions ; Fourier Analysis ; Functional Analysis ; Kernels ; 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, 2020-02, Vol.26 (1), Article 17</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>COPYRIGHT 2020 Springer</rights><rights>2020© Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c436t-e48a2de3eeadac6f6e6dbc4cbccbeda9ed447b4006be59d592ec63339034f11b3</citedby><cites>FETCH-LOGICAL-c436t-e48a2de3eeadac6f6e6dbc4cbccbeda9ed447b4006be59d592ec63339034f11b3</cites><orcidid>0000-0003-2529-5987</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/s00041-019-09719-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-019-09719-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01918516$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Kellay, K.</creatorcontrib><creatorcontrib>Omari, Y.</creatorcontrib><title>Riesz Bases of Reproducing Kernels in Small Fock Spaces</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>We give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock spaces
F
φ
2
, the spaces of entire functions
f
such that
f
e
-
φ
∈
L
2
(
C
)
, where
φ
(
z
)
=
(
log
+
|
z
|
)
β
+
1
,
0
<
β
≤
1
. The first results in this direction are due to Borichev–Lyubarskii who showed that
φ
with
β
=
1
is the largest weight for which the corresponding Fock space admits Riesz bases of reproducing kernels. Later, such bases were characterized by Baranov et al. in the case when
β
=
1
. The present paper answers a question in Baranov et al. by extending their results for all parameters
β
∈
(
0
,
1
)
. Our results are analogous to those obtained for the case
β
=
1
and those proved for Riesz bases of complex exponentials for the Paley–Wiener spaces. We also obtain a description of complete interpolating sequences in small Fock spaces with corresponding uniform norm.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Classical Analysis and ODEs</subject><subject>Complex Variables</subject><subject>Entire functions</subject><subject>Fourier Analysis</subject><subject>Functional Analysis</subject><subject>Kernels</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>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEUhIMoWKt_wFPAk4etySab3RyrWCsWhFbPIZu8ranbTU1aQX-9qSt6k0DyeMwXZgahc0pGlJDyKhJCOM0IlRmRZbr5ARrQgtGsqAp6mGYiZJqFPEYnMa4IySkr2QCVcwfxE1_rCBH7Bs9hE7zdGdct8QOEDtqIXYcXa922eOLNK15stIF4io4a3UY4-3mH6Hly-3QzzWaPd_c341lmOBPbDHilcwsMQFttRCNA2NpwUxtTg9USLOdlzQkRNRTSFjIHIxhjkjDeUFqzIbrs_33RrdoEt9bhQ3nt1HQ8U_tdikxTRPGeJ-1Fr00R3nYQt2rld6FL9lTOOMurqmAiqUa9aqlbUK5r_DZok46FtTO-g8al_bikFeesqEgC8h4wwccYoPn1QYnat6_69vdW1Hf7iieI9VBM4m4J4c_LP9QX3buFyw</recordid><startdate>20200201</startdate><enddate>20200201</enddate><creator>Kellay, K.</creator><creator>Omari, Y.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-2529-5987</orcidid></search><sort><creationdate>20200201</creationdate><title>Riesz Bases of Reproducing Kernels in Small Fock Spaces</title><author>Kellay, K. ; Omari, Y.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c436t-e48a2de3eeadac6f6e6dbc4cbccbeda9ed447b4006be59d592ec63339034f11b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Classical Analysis and ODEs</topic><topic>Complex Variables</topic><topic>Entire functions</topic><topic>Fourier Analysis</topic><topic>Functional Analysis</topic><topic>Kernels</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>Kellay, K.</creatorcontrib><creatorcontrib>Omari, Y.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kellay, K.</au><au>Omari, Y.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Riesz Bases of Reproducing Kernels in Small Fock Spaces</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2020-02-01</date><risdate>2020</risdate><volume>26</volume><issue>1</issue><artnum>17</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>We give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock spaces
F
φ
2
, the spaces of entire functions
f
such that
f
e
-
φ
∈
L
2
(
C
)
, where
φ
(
z
)
=
(
log
+
|
z
|
)
β
+
1
,
0
<
β
≤
1
. The first results in this direction are due to Borichev–Lyubarskii who showed that
φ
with
β
=
1
is the largest weight for which the corresponding Fock space admits Riesz bases of reproducing kernels. Later, such bases were characterized by Baranov et al. in the case when
β
=
1
. The present paper answers a question in Baranov et al. by extending their results for all parameters
β
∈
(
0
,
1
)
. Our results are analogous to those obtained for the case
β
=
1
and those proved for Riesz bases of complex exponentials for the Paley–Wiener spaces. We also obtain a description of complete interpolating sequences in small Fock spaces with corresponding uniform norm.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-019-09719-4</doi><orcidid>https://orcid.org/0000-0003-2529-5987</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | The Journal of fourier analysis and applications, 2020-02, Vol.26 (1), Article 17 |
| issn | 1069-5869 1531-5851 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_01918516v2 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Abstract Harmonic Analysis Approximations and Expansions Classical Analysis and ODEs Complex Variables Entire functions Fourier Analysis Functional Analysis Kernels Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing |
| title | Riesz Bases of Reproducing Kernels in Small Fock Spaces |
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