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Non-Existence of Common Hypercyclic Entire Functions for Certain Families of Translation Operators
Let H ( C ) be the set of entire functions endowed with the topology of local uniform convergence. Fix a sequence of non-zero complex numbers ( λ n ) with lim inf n | λ n + 1 | | λ n | > 2 . We prove that there exists no entire function f such that for every b ∈ C \ { 0 } the set { f ( z + λ n b...
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| Published in: | Computational methods and function theory 2015-09, Vol.15 (3), p.393-401 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c288t-87aca9c09cab2c4531bd007c8b44c39e16352373a8dcc6166398492840299d183 |
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| cites | cdi_FETCH-LOGICAL-c288t-87aca9c09cab2c4531bd007c8b44c39e16352373a8dcc6166398492840299d183 |
| container_end_page | 401 |
| container_issue | 3 |
| container_start_page | 393 |
| container_title | Computational methods and function theory |
| container_volume | 15 |
| creator | Costakis, George Tsirivas, Nikos Vlachou, Vagia |
| description | Let
H
(
C
)
be the set of entire functions endowed with the topology of local uniform convergence. Fix a sequence of non-zero complex numbers
(
λ
n
)
with
lim inf
n
|
λ
n
+
1
|
|
λ
n
|
>
2
.
We prove that there exists no entire function
f
such that for every
b
∈
C
\
{
0
}
the set
{
f
(
z
+
λ
n
b
)
:
n
=
1
,
2
,
…
}
is dense in
H
(
C
)
.
This, on one hand gives a negative answer to Costakis (Approximation by translates of entire functions, Complex and harmonic analysis. Destech Publ., Inc., Lancaster, pp 213–219
2007
, Question 2) and on the other hand shows that certain results from Tsirivas (Existence of common hypercyclic vectors for translation operators,
2014
; Common hypercyclic functions for translation operators with large gaps,
2014
) are sharp. |
| doi_str_mv | 10.1007/s40315-015-0107-1 |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s40315_015_0107_1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s40315_015_0107_1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c288t-87aca9c09cab2c4531bd007c8b44c39e16352373a8dcc6166398492840299d183</originalsourceid><addsrcrecordid>eNp9kEFLAzEQhYMoWKs_wFv-QDSTZHeToyytFYq91POSnWYlZTcpyRbsv3fbevbwGAbeN8x7hDwDfwHOq9esuISC8Yt4xeCGzASYgslKqFsygxIqZpSq7slDznvOC2WknJH2Mwa2-PF5dAEdjR2t4zDEQFeng0t4wt4jXYTRJ0eXx4CjjyHTLiZauzRaH-jSDr73Lp_ZbbIh9_ZsopuJt2NM-ZHcdbbP7ulvzsnXcrGtV2y9ef-o39YMhdYj05VFa5AbtK1AVUhod1My1K1SKI2DUhZCVtLqHWIJZSmNVkZoxYUxO9ByTuB6F1PMObmuOSQ_2HRqgDfnkpprSQ2_aNphYsSVyZM3fLvU7OMxhenNf6BfB71qSg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Non-Existence of Common Hypercyclic Entire Functions for Certain Families of Translation Operators</title><source>Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List</source><creator>Costakis, George ; Tsirivas, Nikos ; Vlachou, Vagia</creator><creatorcontrib>Costakis, George ; Tsirivas, Nikos ; Vlachou, Vagia</creatorcontrib><description>Let
H
(
C
)
be the set of entire functions endowed with the topology of local uniform convergence. Fix a sequence of non-zero complex numbers
(
λ
n
)
with
lim inf
n
|
λ
n
+
1
|
|
λ
n
|
>
2
.
We prove that there exists no entire function
f
such that for every
b
∈
C
\
{
0
}
the set
{
f
(
z
+
λ
n
b
)
:
n
=
1
,
2
,
…
}
is dense in
H
(
C
)
.
This, on one hand gives a negative answer to Costakis (Approximation by translates of entire functions, Complex and harmonic analysis. Destech Publ., Inc., Lancaster, pp 213–219
2007
, Question 2) and on the other hand shows that certain results from Tsirivas (Existence of common hypercyclic vectors for translation operators,
2014
; Common hypercyclic functions for translation operators with large gaps,
2014
) are sharp.</description><identifier>ISSN: 1617-9447</identifier><identifier>EISSN: 2195-3724</identifier><identifier>DOI: 10.1007/s40315-015-0107-1</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Computational Mathematics and Numerical Analysis ; Functions of a Complex Variable ; Mathematics ; Mathematics and Statistics</subject><ispartof>Computational methods and function theory, 2015-09, Vol.15 (3), p.393-401</ispartof><rights>Springer-Verlag Berlin Heidelberg 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-87aca9c09cab2c4531bd007c8b44c39e16352373a8dcc6166398492840299d183</citedby><cites>FETCH-LOGICAL-c288t-87aca9c09cab2c4531bd007c8b44c39e16352373a8dcc6166398492840299d183</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Costakis, George</creatorcontrib><creatorcontrib>Tsirivas, Nikos</creatorcontrib><creatorcontrib>Vlachou, Vagia</creatorcontrib><title>Non-Existence of Common Hypercyclic Entire Functions for Certain Families of Translation Operators</title><title>Computational methods and function theory</title><addtitle>Comput. Methods Funct. Theory</addtitle><description>Let
H
(
C
)
be the set of entire functions endowed with the topology of local uniform convergence. Fix a sequence of non-zero complex numbers
(
λ
n
)
with
lim inf
n
|
λ
n
+
1
|
|
λ
n
|
>
2
.
We prove that there exists no entire function
f
such that for every
b
∈
C
\
{
0
}
the set
{
f
(
z
+
λ
n
b
)
:
n
=
1
,
2
,
…
}
is dense in
H
(
C
)
.
This, on one hand gives a negative answer to Costakis (Approximation by translates of entire functions, Complex and harmonic analysis. Destech Publ., Inc., Lancaster, pp 213–219
2007
, Question 2) and on the other hand shows that certain results from Tsirivas (Existence of common hypercyclic vectors for translation operators,
2014
; Common hypercyclic functions for translation operators with large gaps,
2014
) are sharp.</description><subject>Analysis</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Functions of a Complex Variable</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1617-9447</issn><issn>2195-3724</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQhYMoWKs_wFv-QDSTZHeToyytFYq91POSnWYlZTcpyRbsv3fbevbwGAbeN8x7hDwDfwHOq9esuISC8Yt4xeCGzASYgslKqFsygxIqZpSq7slDznvOC2WknJH2Mwa2-PF5dAEdjR2t4zDEQFeng0t4wt4jXYTRJ0eXx4CjjyHTLiZauzRaH-jSDr73Lp_ZbbIh9_ZsopuJt2NM-ZHcdbbP7ulvzsnXcrGtV2y9ef-o39YMhdYj05VFa5AbtK1AVUhod1My1K1SKI2DUhZCVtLqHWIJZSmNVkZoxYUxO9ByTuB6F1PMObmuOSQ_2HRqgDfnkpprSQ2_aNphYsSVyZM3fLvU7OMxhenNf6BfB71qSg</recordid><startdate>20150901</startdate><enddate>20150901</enddate><creator>Costakis, George</creator><creator>Tsirivas, Nikos</creator><creator>Vlachou, Vagia</creator><general>Springer Berlin Heidelberg</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150901</creationdate><title>Non-Existence of Common Hypercyclic Entire Functions for Certain Families of Translation Operators</title><author>Costakis, George ; Tsirivas, Nikos ; Vlachou, Vagia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-87aca9c09cab2c4531bd007c8b44c39e16352373a8dcc6166398492840299d183</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Analysis</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Functions of a Complex Variable</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Costakis, George</creatorcontrib><creatorcontrib>Tsirivas, Nikos</creatorcontrib><creatorcontrib>Vlachou, Vagia</creatorcontrib><collection>CrossRef</collection><jtitle>Computational methods and function theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Costakis, George</au><au>Tsirivas, Nikos</au><au>Vlachou, Vagia</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-Existence of Common Hypercyclic Entire Functions for Certain Families of Translation Operators</atitle><jtitle>Computational methods and function theory</jtitle><stitle>Comput. Methods Funct. Theory</stitle><date>2015-09-01</date><risdate>2015</risdate><volume>15</volume><issue>3</issue><spage>393</spage><epage>401</epage><pages>393-401</pages><issn>1617-9447</issn><eissn>2195-3724</eissn><abstract>Let
H
(
C
)
be the set of entire functions endowed with the topology of local uniform convergence. Fix a sequence of non-zero complex numbers
(
λ
n
)
with
lim inf
n
|
λ
n
+
1
|
|
λ
n
|
>
2
.
We prove that there exists no entire function
f
such that for every
b
∈
C
\
{
0
}
the set
{
f
(
z
+
λ
n
b
)
:
n
=
1
,
2
,
…
}
is dense in
H
(
C
)
.
This, on one hand gives a negative answer to Costakis (Approximation by translates of entire functions, Complex and harmonic analysis. Destech Publ., Inc., Lancaster, pp 213–219
2007
, Question 2) and on the other hand shows that certain results from Tsirivas (Existence of common hypercyclic vectors for translation operators,
2014
; Common hypercyclic functions for translation operators with large gaps,
2014
) are sharp.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40315-015-0107-1</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1617-9447 |
| ispartof | Computational methods and function theory, 2015-09, Vol.15 (3), p.393-401 |
| issn | 1617-9447 2195-3724 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s40315_015_0107_1 |
| source | Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List |
| subjects | Analysis Computational Mathematics and Numerical Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics |
| title | Non-Existence of Common Hypercyclic Entire Functions for Certain Families of Translation Operators |
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