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Some Results on the Rational Bernstein–Markov Property in the Complex Plane
The Bernstein–Markov property is an asymptotic quantitative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to L μ 2 -norms, where μ is a positive finite measure. We consider two variants of the Bernstein–Markov property for rational funct...
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| Published in: | Computational methods and function theory 2017-09, Vol.17 (3), p.405-443 |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c316t-519c148149535fd66c421fac6c4042d2bd703c9e57682d7c2031ad03b4c634613 |
| container_end_page | 443 |
| container_issue | 3 |
| container_start_page | 405 |
| container_title | Computational methods and function theory |
| container_volume | 17 |
| creator | Piazzon, Federico |
| description | The Bernstein–Markov property is an asymptotic quantitative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to
L
μ
2
-norms, where
μ
is a positive finite measure. We consider two variants of the Bernstein–Markov property for rational functions with restricted poles and compare them with the polynomial Bernstein–Markov property to find some sufficient conditions for the latter to imply the former. Moreover, we recover a sufficient
mass-density
condition for a measure to satisfy the rational Bernstein–Markov property on its support. Finally we present, as an application, a meromorphic
L
2
version of the Bernstein–Walsh Lemma. |
| doi_str_mv | 10.1007/s40315-017-0194-2 |
| format | article |
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L
μ
2
-norms, where
μ
is a positive finite measure. We consider two variants of the Bernstein–Markov property for rational functions with restricted poles and compare them with the polynomial Bernstein–Markov property to find some sufficient conditions for the latter to imply the former. Moreover, we recover a sufficient
mass-density
condition for a measure to satisfy the rational Bernstein–Markov property on its support. Finally we present, as an application, a meromorphic
L
2
version of the Bernstein–Walsh Lemma.</description><identifier>ISSN: 1617-9447</identifier><identifier>EISSN: 2195-3724</identifier><identifier>DOI: 10.1007/s40315-017-0194-2</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Asymptotic properties ; Computational Mathematics and Numerical Analysis ; Functions (mathematics) ; Functions of a Complex Variable ; Markov processes ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Norms ; Polynomials ; Rational functions</subject><ispartof>Computational methods and function theory, 2017-09, Vol.17 (3), p.405-443</ispartof><rights>Springer-Verlag Berlin Heidelberg 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-519c148149535fd66c421fac6c4042d2bd703c9e57682d7c2031ad03b4c634613</citedby><cites>FETCH-LOGICAL-c316t-519c148149535fd66c421fac6c4042d2bd703c9e57682d7c2031ad03b4c634613</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Piazzon, Federico</creatorcontrib><title>Some Results on the Rational Bernstein–Markov Property in the Complex Plane</title><title>Computational methods and function theory</title><addtitle>Comput. Methods Funct. Theory</addtitle><description>The Bernstein–Markov property is an asymptotic quantitative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to
L
μ
2
-norms, where
μ
is a positive finite measure. We consider two variants of the Bernstein–Markov property for rational functions with restricted poles and compare them with the polynomial Bernstein–Markov property to find some sufficient conditions for the latter to imply the former. Moreover, we recover a sufficient
mass-density
condition for a measure to satisfy the rational Bernstein–Markov property on its support. Finally we present, as an application, a meromorphic
L
2
version of the Bernstein–Walsh Lemma.</description><subject>Analysis</subject><subject>Asymptotic properties</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Functions (mathematics)</subject><subject>Functions of a Complex Variable</subject><subject>Markov processes</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Norms</subject><subject>Polynomials</subject><subject>Rational functions</subject><issn>1617-9447</issn><issn>2195-3724</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAQhS0EEqVwAHaRWAc89sSul1DxJ7Wi4mdtuY4DKWlc7BTRHXfghpwEV2HBhsXoaTTfG808Qo6BngKl8iwi5VDkFGQqhTnbIQMGqsi5ZLhLBiDSRCHKfXIQ44LSAhXnAzJ98EuX3bu4brqY-TbrXlJrutq3pskuXGhj5-r2-_NrasKrf89mwa9c6DZZ3bNjv1w17iObNaZ1h2SvMk10R786JE9Xl4_jm3xyd307Pp_kloPo8gKUBRwBqoIXVSmERQaVsUkpspLNS0m5Va6QYsRKaVn6zZSUz9EKjgL4kJz0e1fBv61d7PTCr0O6OGpQTKEUiKNEQU_Z4GMMrtKrUC9N2Gigepua7lPTKTW9TU2z5GG9Jya2fXbhz-Z_TT9LH27I</recordid><startdate>20170901</startdate><enddate>20170901</enddate><creator>Piazzon, Federico</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170901</creationdate><title>Some Results on the Rational Bernstein–Markov Property in the Complex Plane</title><author>Piazzon, Federico</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-519c148149535fd66c421fac6c4042d2bd703c9e57682d7c2031ad03b4c634613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis</topic><topic>Asymptotic properties</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Functions (mathematics)</topic><topic>Functions of a Complex Variable</topic><topic>Markov processes</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Norms</topic><topic>Polynomials</topic><topic>Rational functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Piazzon, Federico</creatorcontrib><collection>CrossRef</collection><jtitle>Computational methods and function theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Piazzon, Federico</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some Results on the Rational Bernstein–Markov Property in the Complex Plane</atitle><jtitle>Computational methods and function theory</jtitle><stitle>Comput. Methods Funct. Theory</stitle><date>2017-09-01</date><risdate>2017</risdate><volume>17</volume><issue>3</issue><spage>405</spage><epage>443</epage><pages>405-443</pages><issn>1617-9447</issn><eissn>2195-3724</eissn><abstract>The Bernstein–Markov property is an asymptotic quantitative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to
L
μ
2
-norms, where
μ
is a positive finite measure. We consider two variants of the Bernstein–Markov property for rational functions with restricted poles and compare them with the polynomial Bernstein–Markov property to find some sufficient conditions for the latter to imply the former. Moreover, we recover a sufficient
mass-density
condition for a measure to satisfy the rational Bernstein–Markov property on its support. Finally we present, as an application, a meromorphic
L
2
version of the Bernstein–Walsh Lemma.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40315-017-0194-2</doi><tpages>39</tpages></addata></record> |
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| ispartof | Computational methods and function theory, 2017-09, Vol.17 (3), p.405-443 |
| issn | 1617-9447 2195-3724 |
| language | eng |
| recordid | cdi_proquest_journals_1929476448 |
| source | Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List |
| subjects | Analysis Asymptotic properties Computational Mathematics and Numerical Analysis Functions (mathematics) Functions of a Complex Variable Markov processes Mathematical analysis Mathematics Mathematics and Statistics Norms Polynomials Rational functions |
| title | Some Results on the Rational Bernstein–Markov Property in the Complex Plane |
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