Some remarks on approximation in several complex variables
In Gauthier, Manolaki, and Nestoridis (2021, Advances in Mathematics 381, 107649), in order to correct a false Mergelyan-type statement given in Gamelin and Garnett (1969, Transactions of the American Mathematical Society 143, 187–200) on uniform approximation on compact sets K in $\mathbb C^d$ , th...
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| Veröffentlicht in: | Canadian mathematical bulletin 2023-06, Vol.66 (2), p.643-653 |
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| creator | Falcó, Javier Gauthier, Paul M. Manolaki, Myrto Nestoridis, Vassili |
| description | In Gauthier, Manolaki, and Nestoridis (2021, Advances in Mathematics 381, 107649), in order to correct a false Mergelyan-type statement given in Gamelin and Garnett (1969, Transactions of the American Mathematical Society 143, 187–200) on uniform approximation on compact sets K in
$\mathbb C^d$
, the authors introduced a natural function algebra
$A_D(K)$
which is smaller than the classical one
$A(K)$
. In the present paper, we investigate when these two algebras coincide and compare them with the classes of all plausibly approximable functions by polynomials or rational functions or functions holomorphic on open sets containing the compact set K. Finally, we introduce a notion of O-hull of K and strengthen known results. |
| doi_str_mv | 10.4153/S0008439522000613 |
| format | Article |
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$\mathbb C^d$
, the authors introduced a natural function algebra
$A_D(K)$
which is smaller than the classical one
$A(K)$
. In the present paper, we investigate when these two algebras coincide and compare them with the classes of all plausibly approximable functions by polynomials or rational functions or functions holomorphic on open sets containing the compact set K. Finally, we introduce a notion of O-hull of K and strengthen known results.</description><identifier>ISSN: 0008-4395</identifier><identifier>EISSN: 1496-4287</identifier><identifier>DOI: 10.4153/S0008439522000613</identifier><language>eng</language><publisher>Canada: Canadian Mathematical Society</publisher><subject>Algebra ; Approximation ; Complex variables ; Equality ; Mathematical analysis ; Polynomials ; Rational functions</subject><ispartof>Canadian mathematical bulletin, 2023-06, Vol.66 (2), p.643-653</ispartof><rights>The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society</rights><rights>The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society. This work is licensed under the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c312t-23d33a812a3c1e6ae18465cf8d7fb302bcdfe8c198b52380af9928fdcfad39243</cites><orcidid>0000-0001-5435-3053</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0008439522000613/type/journal_article$$EHTML$$P50$$Gcambridge$$Hfree_for_read</linktohtml><link.rule.ids>164,314,776,780,27901,27902,55603</link.rule.ids></links><search><creatorcontrib>Falcó, Javier</creatorcontrib><creatorcontrib>Gauthier, Paul M.</creatorcontrib><creatorcontrib>Manolaki, Myrto</creatorcontrib><creatorcontrib>Nestoridis, Vassili</creatorcontrib><title>Some remarks on approximation in several complex variables</title><title>Canadian mathematical bulletin</title><addtitle>Can. Math. Bull</addtitle><description>In Gauthier, Manolaki, and Nestoridis (2021, Advances in Mathematics 381, 107649), in order to correct a false Mergelyan-type statement given in Gamelin and Garnett (1969, Transactions of the American Mathematical Society 143, 187–200) on uniform approximation on compact sets K in
$\mathbb C^d$
, the authors introduced a natural function algebra
$A_D(K)$
which is smaller than the classical one
$A(K)$
. In the present paper, we investigate when these two algebras coincide and compare them with the classes of all plausibly approximable functions by polynomials or rational functions or functions holomorphic on open sets containing the compact set K. 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$\mathbb C^d$
, the authors introduced a natural function algebra
$A_D(K)$
which is smaller than the classical one
$A(K)$
. In the present paper, we investigate when these two algebras coincide and compare them with the classes of all plausibly approximable functions by polynomials or rational functions or functions holomorphic on open sets containing the compact set K. Finally, we introduce a notion of O-hull of K and strengthen known results.</abstract><cop>Canada</cop><pub>Canadian Mathematical Society</pub><doi>10.4153/S0008439522000613</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0001-5435-3053</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Canadian mathematical bulletin, 2023-06, Vol.66 (2), p.643-653 |
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| language | eng |
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| source | Cambridge University Press Journals Complete |
| subjects | Algebra Approximation Complex variables Equality Mathematical analysis Polynomials Rational functions |
| title | Some remarks on approximation in several complex variables |
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