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Surjectivity of linear operators and semialgebraic global diffeomorphisms
We prove that a C ∞ semialgebraic local diffeomorphism of ℝ n with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if n − 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeo...
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| Published in: | Journal d'analyse mathématique (Jerusalem) 2023-09, Vol.150 (2), p.789-802 |
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| Main Authors: | , , |
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| Language: | English |
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| container_end_page | 802 |
| container_issue | 2 |
| container_start_page | 789 |
| container_title | Journal d'analyse mathématique (Jerusalem) |
| container_volume | 150 |
| creator | Braun, Francisco Dias, Luis Renato Goncalves Venato-Santos, Jean |
| description | We prove that a
C
∞ semialgebraic local diffeomorphism of ℝ
n
with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if
n
− 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of ℝ
n
. Our conjecture implies a very known conjecture of
Z
. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature. |
| doi_str_mv | 10.1007/s11854-023-0286-z |
| format | article |
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C
∞ semialgebraic local diffeomorphism of ℝ
n
with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if
n
− 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of ℝ
n
. Our conjecture implies a very known conjecture of
Z
. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature.</description><identifier>ISSN: 0021-7670</identifier><identifier>EISSN: 1565-8538</identifier><identifier>DOI: 10.1007/s11854-023-0286-z</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Abstract Harmonic Analysis ; Analysis ; Differential equations ; Dynamical Systems and Ergodic Theory ; Functional Analysis ; Isomorphism ; Linear operators ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Partial Differential Equations ; Polynomials</subject><ispartof>Journal d'analyse mathématique (Jerusalem), 2023-09, Vol.150 (2), p.789-802</ispartof><rights>The Hebrew University of Jerusalem 2023</rights><rights>The Hebrew University of Jerusalem 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-c2e7d7578c98a967be3c7281e58a7dacef082bdf6e47e9c80dd49144cc72150e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Braun, Francisco</creatorcontrib><creatorcontrib>Dias, Luis Renato Goncalves</creatorcontrib><creatorcontrib>Venato-Santos, Jean</creatorcontrib><title>Surjectivity of linear operators and semialgebraic global diffeomorphisms</title><title>Journal d'analyse mathématique (Jerusalem)</title><addtitle>JAMA</addtitle><description>We prove that a
C
∞ semialgebraic local diffeomorphism of ℝ
n
with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if
n
− 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of ℝ
n
. Our conjecture implies a very known conjecture of
Z
. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature.</description><subject>Abstract Harmonic Analysis</subject><subject>Analysis</subject><subject>Differential equations</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Functional Analysis</subject><subject>Isomorphism</subject><subject>Linear operators</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Partial Differential Equations</subject><subject>Polynomials</subject><issn>0021-7670</issn><issn>1565-8538</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAQhoMouK7-AG8Bz9UkbT56lMWPBcGDeg5pOlmztE1NusLurzdLBU8eZubyvDPMg9A1JbeUEHmXKFW8KggrcylRHE7QgnLBC8VLdYoWhDBaSCHJObpIaUsI53XJFmj9totbsJP_9tMeB4c7P4CJOIwQzRRiwmZocYLem24DTTTe4k0XGtPh1jsHoQ9x_PSpT5fozJkuwdXvXKKPx4f31XPx8vq0Xt2_FJYJNeUOspVcKlsrUwvZQGklUxS4MrI1FhxRrGmdgEpCbRVp26qmVWUzRTmBcolu5r1jDF87SJPehl0c8kmdH5dclUKJTNGZsjGkFMHpMfrexL2mRB-N6dmYzsb00Zg-5AybMymzwwbi3-b_Qz8x43Ac</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Braun, Francisco</creator><creator>Dias, Luis Renato Goncalves</creator><creator>Venato-Santos, Jean</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20230901</creationdate><title>Surjectivity of linear operators and semialgebraic global diffeomorphisms</title><author>Braun, Francisco ; Dias, Luis Renato Goncalves ; Venato-Santos, Jean</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-c2e7d7578c98a967be3c7281e58a7dacef082bdf6e47e9c80dd49144cc72150e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Analysis</topic><topic>Differential equations</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Functional Analysis</topic><topic>Isomorphism</topic><topic>Linear operators</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Partial Differential Equations</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Braun, Francisco</creatorcontrib><creatorcontrib>Dias, Luis Renato Goncalves</creatorcontrib><creatorcontrib>Venato-Santos, Jean</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Braun, Francisco</au><au>Dias, Luis Renato Goncalves</au><au>Venato-Santos, Jean</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Surjectivity of linear operators and semialgebraic global diffeomorphisms</atitle><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle><stitle>JAMA</stitle><date>2023-09-01</date><risdate>2023</risdate><volume>150</volume><issue>2</issue><spage>789</spage><epage>802</epage><pages>789-802</pages><issn>0021-7670</issn><eissn>1565-8538</eissn><abstract>We prove that a
C
∞ semialgebraic local diffeomorphism of ℝ
n
with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if
n
− 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of ℝ
n
. Our conjecture implies a very known conjecture of
Z
. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11854-023-0286-z</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-7670 |
| ispartof | Journal d'analyse mathématique (Jerusalem), 2023-09, Vol.150 (2), p.789-802 |
| issn | 0021-7670 1565-8538 |
| language | eng |
| recordid | cdi_proquest_journals_2867583686 |
| source | Springer Nature |
| subjects | Abstract Harmonic Analysis Analysis Differential equations Dynamical Systems and Ergodic Theory Functional Analysis Isomorphism Linear operators Mathematics Mathematics and Statistics Operators (mathematics) Partial Differential Equations Polynomials |
| title | Surjectivity of linear operators and semialgebraic global diffeomorphisms |
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