The complex moment problem: determinacy and extendibility
Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is determinate and its only representing measure has no atom a...
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| creator | Cichoń, D Szafraniec, J. Stochel. F. H |
| description | Complex moment sequences are exactly those which admit positive definite
extensions on the integer lattice points of the upper diagonal half-plane. Here
we prove that the aforesaid extension is unique provided the complex moment
sequence is determinate and its only representing measure has no atom at $0$.
The question of converting the relation is posed as an open problem. A partial
solution to this problem is established when at least one of representing
measures is supported in a plane algebraic curve whose intersection with every
straight line passing through $0$ is at most one point set. Further study
concerns representing measures whose supports are Zariski dense in $\mathbb C$
as well as complex moment sequences which are constant on a family of parallel
"Diophantine lines". All this is supported by a bunch of illustrative examples. |
| doi_str_mv | 10.48550/arxiv.1803.03066 |
| format | Article |
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extensions on the integer lattice points of the upper diagonal half-plane. Here
we prove that the aforesaid extension is unique provided the complex moment
sequence is determinate and its only representing measure has no atom at $0$.
The question of converting the relation is posed as an open problem. A partial
solution to this problem is established when at least one of representing
measures is supported in a plane algebraic curve whose intersection with every
straight line passing through $0$ is at most one point set. Further study
concerns representing measures whose supports are Zariski dense in $\mathbb C$
as well as complex moment sequences which are constant on a family of parallel
"Diophantine lines". All this is supported by a bunch of illustrative examples.</description><identifier>DOI: 10.48550/arxiv.1803.03066</identifier><language>eng</language><subject>Mathematics - Functional Analysis</subject><creationdate>2018-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1803.03066$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1803.03066$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Cichoń, D</creatorcontrib><creatorcontrib>Szafraniec, J. Stochel. F. H</creatorcontrib><title>The complex moment problem: determinacy and extendibility</title><description>Complex moment sequences are exactly those which admit positive definite
extensions on the integer lattice points of the upper diagonal half-plane. Here
we prove that the aforesaid extension is unique provided the complex moment
sequence is determinate and its only representing measure has no atom at $0$.
The question of converting the relation is posed as an open problem. A partial
solution to this problem is established when at least one of representing
measures is supported in a plane algebraic curve whose intersection with every
straight line passing through $0$ is at most one point set. Further study
concerns representing measures whose supports are Zariski dense in $\mathbb C$
as well as complex moment sequences which are constant on a family of parallel
"Diophantine lines". All this is supported by a bunch of illustrative examples.</description><subject>Mathematics - Functional Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj71qwzAURrVkKEkfoFP1AnalKLpSsoXQPwh08W6upCsisGyjmGK_fdO00zcc-DiHsScp6p3VWrxgmdN3La1QtVAC4IHtmwtxP-Sxo5nnIVM_8bEMrqN84IEmKjn16BeOfeA0T9SH5FKXpmXDVhG7Kz3-75o1b6_N6aM6f71_no7nCsFAFUJ0JILzUodt9AhBbjF6AIlRWQ0EzhhnY7A7FzFGrW_cGXXTs2ZvvFqz57_bu3s7lpSxLO1vQ3tvUD-cLkLk</recordid><startdate>20180308</startdate><enddate>20180308</enddate><creator>Cichoń, D</creator><creator>Szafraniec, J. Stochel. F. H</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20180308</creationdate><title>The complex moment problem: determinacy and extendibility</title><author>Cichoń, D ; Szafraniec, J. Stochel. F. H</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-ddfbe0dbc15d2fca6d12afc661af3856e6b77b8fd84bfaff5512ab730308797c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Mathematics - Functional Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Cichoń, D</creatorcontrib><creatorcontrib>Szafraniec, J. Stochel. F. H</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Cichoń, D</au><au>Szafraniec, J. Stochel. F. H</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The complex moment problem: determinacy and extendibility</atitle><date>2018-03-08</date><risdate>2018</risdate><abstract>Complex moment sequences are exactly those which admit positive definite
extensions on the integer lattice points of the upper diagonal half-plane. Here
we prove that the aforesaid extension is unique provided the complex moment
sequence is determinate and its only representing measure has no atom at $0$.
The question of converting the relation is posed as an open problem. A partial
solution to this problem is established when at least one of representing
measures is supported in a plane algebraic curve whose intersection with every
straight line passing through $0$ is at most one point set. Further study
concerns representing measures whose supports are Zariski dense in $\mathbb C$
as well as complex moment sequences which are constant on a family of parallel
"Diophantine lines". All this is supported by a bunch of illustrative examples.</abstract><doi>10.48550/arxiv.1803.03066</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Functional Analysis |
| title | The complex moment problem: determinacy and extendibility |
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