On Polynomial Sequences with Restricted Growth near Infinity
Identifieur interne : 001759 ( Istex/Corpus ); précédent : 001758; suivant : 001760On Polynomial Sequences with Restricted Growth near Infinity
Auteurs : J. Müller ; A. YavrianSource :
- Bulletin of the London Mathematical Society [ 0024-6093 ] ; 2002-03.
Abstract
Let (Pn) be a sequence of polynomials which converges with a geometric rate on some arc in the complex plane to an analytic function. It is shown that if the sequence has restricted growth on a closed plane set E which is non-thin at ∞, then the limit function has a maximal domain of existence, and (Pn) converges with a locally geometric rate on this domain. If (Snk) is a sequence of partial sums of a power series, a similar growth restriction on E forces the power series to have Ostrowski gaps. Moreover, the requirement of non-thinness of E at ∞ is necessary for these conclusions.
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DOI: 10.1112/S0024609301008803
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Yavrian</name><affiliation><mods:affiliation>Yerevan State University, Dept. of Mathematics Alex Manoogian Str. 1, 375049 Yerevan, Armenia; ayavrian@ysu.am</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: ayavrian@ysu.am</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9</idno><date when="2002" year="2002">2002</date><idno type="doi">10.1112/S0024609301008803</idno><idno type="url">https://api.istex.fr/document/3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001759</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001759</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">On Polynomial Sequences with Restricted Growth near Infinity</title><author><name sortKey="Muller, J" sort="Muller, J" uniqKey="Muller J" first="J." last="Müller">J. Müller</name><affiliation><mods:affiliation>University of Trier FB IV, Mathematics, D-54286 Trier, Germany; jmueller@uni-trier.de</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: jmueller@uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Yavrian, A" sort="Yavrian, A" uniqKey="Yavrian A" first="A." last="Yavrian">A. Yavrian</name><affiliation><mods:affiliation>Yerevan State University, Dept. of Mathematics Alex Manoogian Str. 1, 375049 Yerevan, Armenia; ayavrian@ysu.am</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: ayavrian@ysu.am</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Bulletin of the London Mathematical Society</title><idno type="ISSN">0024-6093</idno><idno type="eISSN">1469-2120</idno><imprint><publisher>Oxford University Press</publisher><date type="published" when="2002-03">2002-03</date><biblScope unit="volume">34</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="189">189</biblScope><biblScope unit="page" to="199">199</biblScope></imprint><idno type="ISSN">0024-6093</idno></series><idno type="istex">3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9</idno><idno type="DOI">10.1112/S0024609301008803</idno><idno type="ArticleID">34.2.189</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0024-6093</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract">Let (Pn) be a sequence of polynomials which converges with a geometric rate on some arc in the complex plane to an analytic function. It is shown that if the sequence has restricted growth on a closed plane set E which is non-thin at ∞, then the limit function has a maximal domain of existence, and (Pn) converges with a locally geometric rate on this domain. If (Snk) is a sequence of partial sums of a power series, a similar growth restriction on E forces the power series to have Ostrowski gaps. Moreover, the requirement of non-thinness of E at ∞ is necessary for these conclusions.</div></front></TEI><istex><corpusName>oup</corpusName><author><json:item><name>J. Müller</name><affiliations><json:string>University of Trier FB IV, Mathematics, D-54286 Trier, Germany; jmueller@uni-trier.de</json:string><json:string>E-mail: jmueller@uni-trier.de</json:string></affiliations></json:item><json:item><name>A. Yavrian</name><affiliations><json:string>Yerevan State University, Dept. of Mathematics Alex Manoogian Str. 1, 375049 Yerevan, Armenia; ayavrian@ysu.am</json:string><json:string>E-mail: ayavrian@ysu.am</json:string></affiliations></json:item></author><subject><json:item><value>Papers</value></json:item></subject><articleId><json:string>34.2.189</json:string></articleId><language><json:string>unknown</json:string></language><originalGenre><json:string>research-article</json:string></originalGenre><abstract>Let (Pn) be a sequence of polynomials which converges with a geometric rate on some arc in the complex plane to an analytic function. It is shown that if the sequence has restricted growth on a closed plane set E which is non-thin at ∞, then the limit function has a maximal domain of existence, and (Pn) converges with a locally geometric rate on this domain. If (Snk) is a sequence of partial sums of a power series, a similar growth restriction on E forces the power series to have Ostrowski gaps. Moreover, the requirement of non-thinness of E at ∞ is necessary for these conclusions.</abstract><qualityIndicators><score>7.33</score><pdfVersion>1.2</pdfVersion><pdfPageSize>595 x 841 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>1</keywordCount><abstractCharCount>588</abstractCharCount><pdfWordCount>4058</pdfWordCount><pdfCharCount>17502</pdfCharCount><pdfPageCount>11</pdfPageCount><abstractWordCount>106</abstractWordCount></qualityIndicators><title>On Polynomial Sequences with Restricted Growth near Infinity</title><refBibs><json:item><author><json:item><name>V,A Beljaev</name></json:item></author><host><volume>24</volume><pages><last>538</last><first>533</first></pages><author></author><title>Math. 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Giessen</title><publicationDate>1994</publicationDate></host><publicationDate>1994</publicationDate></json:item><json:item><host><pages><last>90</last><first>81</first></pages><author><json:item><name>W Gehlen</name></json:item><json:item><name>W Luh</name></json:item><json:item><name>J Müller</name></json:item></author><title>On the existence of O-universal functions, Complex Variables Theory Appl</title><publicationDate>2000</publicationDate></host></json:item><json:item><author><json:item><name>W,K Hayman</name></json:item><json:item><name>P,B Kennedy</name></json:item></author><host><author></author><title>Subharmonic functions</title><publicationDate>1976</publicationDate></host><publicationDate>1976</publicationDate></json:item><json:item><host><author><json:item><name>E Hille</name></json:item></author><title>Analytic function theory</title><publicationDate>1987</publicationDate></host></json:item><json:item><author><json:item><name>P,P Korovkin</name></json:item></author><host><volume>78</volume><pages><last>1084</last><first>1081</first></pages><author></author><title>Dokl. Akad. Nauk USSR</title><publicationDate>1951</publicationDate></host><title>On the growth of functions</title><publicationDate>1951</publicationDate></json:item><json:item><author><json:item><name>J Marcinkiewicz</name></json:item><json:item><name>A Zygmund</name></json:item></author><host><author></author><title>J. Marcinkiewicz</title><publicationDate>1964</publicationDate></host><title>Sur les series de puissances</title><publicationDate>1964</publicationDate></json:item><json:item><host><author><json:item><name>T Ransford</name></json:item></author><title>Potential theory in the complex plane</title><publicationDate>1995</publicationDate></host></json:item><json:item><author><json:item><name>M Tsuji</name></json:item></author><host><author></author><title>Potential theory in modern function theory</title><publicationDate>1975</publicationDate></host><publicationDate>1975</publicationDate></json:item><json:item><author><json:item><name>L,L Walsh</name></json:item></author><host><volume>13</volume><pages><last>234</last><first>195</first></pages><issue>1</issue><author></author><title>J</title><publicationDate>1946</publicationDate></host><title>Overconvergence, degree of convergence, and zeros of sequences of analytic functions', Duke Math</title><publicationDate>1946</publicationDate></json:item><json:item><author></author><host><author></author><title>Yerevan Armenia ayavrian@ysu.am</title></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>34</volume><publisherId><json:string>blms</json:string></publisherId><pages><last>199</last><first>189</first></pages><issn><json:string>0024-6093</json:string></issn><issue>2</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1469-2120</json:string></eissn><title>Bulletin of the London Mathematical Society</title></host><categories><wos><json:string>science</json:string><json:string>mathematics</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>general mathematics</json:string></scienceMetrix></categories><publicationDate>2002</publicationDate><copyrightDate>2002</copyrightDate><doi><json:string>10.1112/S0024609301008803</json:string></doi><id>3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9</id><score>1.070847</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">On Polynomial Sequences with Restricted Growth near Infinity</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Oxford University Press</publisher><availability><p>© London Mathematical Society</p></availability><date>2002</date></publicationStmt><notesStmt><note>The research of the second author has been supported by the German Academic Exchange Service (DAAD).</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">On Polynomial Sequences with Restricted Growth near Infinity</title><author xml:id="author-1"><persName><forename type="first">J.</forename><surname>Müller</surname></persName><email>jmueller@uni-trier.de</email><affiliation>University of Trier FB IV, Mathematics, D-54286 Trier, Germany; jmueller@uni-trier.de</affiliation></author><author xml:id="author-2"><persName><forename type="first">A.</forename><surname>Yavrian</surname></persName><email>ayavrian@ysu.am</email><note type="biography">The research of the second author has been supported by the German Academic Exchange Service (DAAD).</note><affiliation>The research of the second author has been supported by the German Academic Exchange Service (DAAD).</affiliation><affiliation>Yerevan State University, Dept. of Mathematics Alex Manoogian Str. 1, 375049 Yerevan, Armenia; ayavrian@ysu.am</affiliation></author></analytic><monogr><title level="j">Bulletin of the London Mathematical Society</title><idno type="pISSN">0024-6093</idno><idno type="eISSN">1469-2120</idno><imprint><publisher>Oxford University Press</publisher><date type="published" when="2002-03"></date><biblScope unit="volume">34</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="189">189</biblScope><biblScope unit="page" to="199">199</biblScope></imprint></monogr><idno type="istex">3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9</idno><idno type="DOI">10.1112/S0024609301008803</idno><idno type="ArticleID">34.2.189</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2002</date></creation><abstract><p>Let (Pn) be a sequence of polynomials which converges with a geometric rate on some arc in the complex plane to an analytic function. It is shown that if the sequence has restricted growth on a closed plane set E which is non-thin at ∞, then the limit function has a maximal domain of existence, and (Pn) converges with a locally geometric rate on this domain. If (Snk) is a sequence of partial sums of a power series, a similar growth restriction on E forces the power series to have Ostrowski gaps. 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It is shown that if the sequence has restricted growth on a closed plane set <italic>E</italic> which is non-thin at ∞, then the limit function has a maximal domain of existence, and (<italic>P</italic><sub><italic>n</italic></sub>) converges with a locally geometric rate on this domain. If <inline-formula><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a sequence of partial sums of a power series, a similar growth restriction on <italic>E</italic> forces the power series to have Ostrowski gaps. Moreover, the requirement of non-thinness of <italic>E</italic> at ∞ is necessary for these conclusions.</p></abstract></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>On Polynomial Sequences with Restricted Growth near Infinity</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>On Polynomial Sequences with Restricted Growth near Infinity</title></titleInfo><name type="personal"><namePart type="given">J.</namePart><namePart type="family">Müller</namePart><affiliation>University of Trier FB IV, Mathematics, D-54286 Trier, Germany; jmueller@uni-trier.de</affiliation><affiliation>E-mail: jmueller@uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Yavrian</namePart><affiliation>Yerevan State University, Dept. of Mathematics Alex Manoogian Str. 1, 375049 Yerevan, Armenia; ayavrian@ysu.am</affiliation><affiliation>E-mail: ayavrian@ysu.am</affiliation><description>The research of the second author has been supported by the German Academic Exchange Service (DAAD).</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><subject><topic>Papers</topic></subject><originInfo><publisher>Oxford University Press</publisher><dateIssued encoding="w3cdtf">2002-03</dateIssued><copyrightDate encoding="w3cdtf">2002</copyrightDate></originInfo><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract>Let (Pn) be a sequence of polynomials which converges with a geometric rate on some arc in the complex plane to an analytic function. It is shown that if the sequence has restricted growth on a closed plane set E which is non-thin at ∞, then the limit function has a maximal domain of existence, and (Pn) converges with a locally geometric rate on this domain. If (Snk) is a sequence of partial sums of a power series, a similar growth restriction on E forces the power series to have Ostrowski gaps. Moreover, the requirement of non-thinness of E at ∞ is necessary for these conclusions.</abstract><note type="footnotes">The research of the second author has been supported by the German Academic Exchange Service (DAAD).</note><relatedItem type="host"><titleInfo><title>Bulletin of the London Mathematical Society</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0024-6093</identifier><identifier type="eISSN">1469-2120</identifier><identifier type="PublisherID">blms</identifier><identifier type="PublisherID-hwp">blms</identifier><part><date>2002</date><detail type="volume"><caption>vol.</caption><number>34</number></detail><detail type="issue"><caption>no.</caption><number>2</number></detail><extent unit="pages"><start>189</start><end>199</end></extent></part></relatedItem><identifier type="istex">3172E7B4BDAC57CDFC2BBB7D9C90FCD79798EBA9</identifier><identifier type="DOI">10.1112/S0024609301008803</identifier><identifier type="ArticleID">34.2.189</identifier><accessCondition type="use and reproduction" contentType="copyright">© London Mathematical Society</accessCondition><recordInfo><recordContentSource>OUP</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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