Boundary Estimates for Bergman Polynomials in Domains with Corners
Let The asymptotic behaviour of
Saved in:
| Published in | Modern Trends in Constructive Function Theory Vol. 661; pp. 187 - 198 |
|---|---|
| Main Author | |
| Format | Book Chapter |
| Language | English |
| Published |
Providence, Rhode Island
American Mathematical Society
31.03.2016
|
| Series | Contemporary Mathematics |
| Online Access | Get full text |
| ISBN | 1470425343 9781470425340 |
| ISSN | 0271-4132 1098-3627 |
| DOI | 10.1090/conm/661/13282 |
Cover
| Abstract | Let
The asymptotic behaviour
of |
|---|---|
| AbstractList | Let
The asymptotic behaviour
of |
| Author | Stylianopoulos, N. |
| Author_xml | – sequence: 1 givenname: N. surname: Stylianopoulos fullname: Stylianopoulos, N. email: nikos@ucy.ac.cy organization: Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus |
| BookMark | eNotkD1PwzAQhg0URFq6MntkCfX52yMt5UOqBAPMlpM4NNDYJU6F-u9JKbfc8L7P6fSM0SjE4BG6BnILxJBZGUM7kxJmwKimJ2hqlAauCKeGcX2KsqGlcyapOkPjYyAYZyOUEaog5wN2gTJjmJIUtL5E05Q-yTCcUC4gQ_N53IXKdXu8TH3Tut4nXMcOz3330bqAX-NmH2LbuE3CTcD3sXVNSPin6dd4Ebvgu3SFzush9tP_PUHvD8u3xVO-enl8XtytckcZ7XMnRaGVNMQzpl0piCqZ03VVAYiKgXS18UJWHKDgUjojaqBiqHMqi1qIgk0QO97ddvF751NvfRHjV-lD37lNuXbbfvjGckNAGWIVs2D0QN0cKdemI5AsEHuwaw927WDX_tllv3d8Zzk |
| ContentType | Book Chapter |
| DBID | FFUUA |
| DEWEY | 511.3/26 |
| DOI | 10.1090/conm/661/13282 |
| DatabaseName | ProQuest Ebook Central - Book Chapters - Demo use only |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISBN | 9781470429348 1470429349 |
| EISSN | 1098-3627 |
| Editor | Lubinsky, Doron S. Simanek, Brian Z. Hardin, Douglas P. |
| Editor_xml | – sequence: 1 givenname: Douglas P. surname: Hardin fullname: Hardin, Douglas P. organization: Vanderbilt University, Nashville, TN – sequence: 2 givenname: Doron S. surname: Lubinsky fullname: Lubinsky, Doron S. organization: Georgia Institute of Technology, Atlanta, GA – sequence: 3 givenname: Brian Z. surname: Simanek fullname: Simanek, Brian Z. organization: Vanderbilt University, Nashville, TN |
| EndPage | 198 |
| ExternalDocumentID | EBC4901790_73_198 10_1090_conm_661_13282 |
| GroupedDBID | AABBV AAWPO ABARN ABQPQ ACLGV ADVEM AERYV AFOJC AHWGJ AJFER ALMA_UNASSIGNED_HOLDINGS AZZ BBABE CZZ GEOUK S5T FFUUA |
| ID | FETCH-LOGICAL-a232t-a65b87690e338ac507c3a8fdd115d316af9e56d411b466a95f125690426bf55b3 |
| ISBN | 1470425343 9781470425340 |
| ISSN | 0271-4132 |
| IngestDate | Thu May 29 01:14:36 EDT 2025 Thu Aug 14 15:25:12 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| LCCallNum | QA331.M677 2016 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-a232t-a65b87690e338ac507c3a8fdd115d316af9e56d411b466a95f125690426bf55b3 |
| OCLC | 993762188 |
| PQID | EBC4901790_73_198 |
| PageCount | 12 |
| ParticipantIDs | proquest_ebookcentralchapters_4901790_73_198 ams_ebooks_10_1090_conm_661_13282 |
| PublicationCentury | 2000 |
| PublicationDate | 20160331 2016 |
| PublicationDateYYYYMMDD | 2016-03-31 2016-01-01 |
| PublicationDate_xml | – month: 3 year: 2016 text: 20160331 day: 31 |
| PublicationDecade | 2010 |
| PublicationPlace | Providence, Rhode Island |
| PublicationPlace_xml | – name: Providence, Rhode Island – name: United States |
| PublicationSeriesTitle | Contemporary Mathematics |
| PublicationTitle | Modern Trends in Constructive Function Theory |
| PublicationYear | 2016 |
| Publisher | American Mathematical Society |
| Publisher_xml | – name: American Mathematical Society |
| References | Vladimir V. Andrievskii and Hans-Peter Blatt, Discrepancy of signed measures and polynomial approximation, Springer Monographs in Mathematics, Springer-Verlag, New York, 2002. MR 1871219 (2002k:30001), DOI 10.1007/978-1-4757-4999-1 G. Szegö, Über einen Satz von A. Markoff, Math. Z. 23 (1925), no. 1, 45–61 (German). MR 1544730, DOI 10.1007/BF01506220 V. V. Andrievskii, V. I. Belyi, and V. K. Dzjadyk, Conformal invariants in constructive theory of functions of complex variable, Advanced Series in Mathematical Science and Engineering, vol. 1, World Federation Publishers Company, Atlanta, GA, 1995. Translated from the Russian by D. N. Kravchuk. MR 1421773 (98j:30041) Nikos Stylianopoulos, Strong asymptotics for Bergman polynomials over domains with corners and applications, Constr. Approx. 38 (2013), no. 1, 59–100. MR 3078274, DOI 10.1007/s00365-012-9174-y Ch. Pommerenke, Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 299, Springer-Verlag, Berlin, 1992. MR 1217706 (95b:30008), DOI 10.1007/978-3-662-02770-7 A. C. Schaeffer and G. Szegö, Polynomials whose real part is bounded on a given curve in the complex plane, Amer. J. Math. 62 (1940), 868–876. MR 0002604 (2,83a) Dieter Gaier, The Faber operator and its boundedness, J. Approx. Theory 101 (1999), no. 2, 265–277. MR 1726457 (2000i:41028), DOI 10.1006/jath.1999.3400 V. I. Belyĭ, Conformal mappings and approximation of analytic functions in domains with quasiconformal boundary, Mat. Sb. (N.S.) 102(144) (1977), no. 3, 331–361 (Russian). MR 0460648 (57 \#641) Igor E. Pritsker, Derivatives of Faber polynomials and Markov inequalities, J. Approx. Theory 118 (2002), no. 2, 163–174. MR 1932572 (2003g:30007), DOI 10.1006/jath.2002.3713 E. B. Saff and N. Stylianopoulos, On the zeros of asymptotically extremal polynomial sequences in the plane, J. Approx. Theory 191 (2015), 118–127. MR 3306314, DOI 10.1016/j.jat.2014.10.003 F. G. Abdullaev, On some properties of polynomials, orthogonal with respect to area, in domains of the complex plane. I, Ukraïn. Mat. Zh. 52 (2000), no. 12, 1587–1595 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 52 (2000), no. 12, 1807–1817 (2001). MR 1834619 (2002c:30005), DOI 10.1023/A:1010491406926 P. K. Suetin, Polynomials orthogonal over a region and Bieberbach polynomials, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by R. P. Boas. MR 0463793 (57 \#3732b) R. Sherman Lehman, Development of the mapping function at an analytic corner, Pacific J. Math. 7 (1957), 1437–1449. MR 0095259 (20 \#1765) Vilmos Totik, Christoffel functions on curves and domains, Trans. Amer. Math. Soc. 362 (2010), no. 4, 2053–2087. MR 2574887 (2011b:30006), DOI 10.1090/S0002-9947-09-05059-4 Igor E. Pritsker, Comparing norms of polynomials in one and several variables, J. Math. Anal. Appl. 216 (1997), no. 2, 685–695. MR 1489606 (98j:30002), DOI 10.1006/jmaa.1997.5699 Dieter Gaier, On a polynomial lemma of Andrievskiĭ, Arch. Math. (Basel) 49 (1987), no. 2, 119–123. MR 901822 (89d:30005), DOI 10.1007/BF01200474 |
| References_xml | – reference: Vladimir V. Andrievskii and Hans-Peter Blatt, Discrepancy of signed measures and polynomial approximation, Springer Monographs in Mathematics, Springer-Verlag, New York, 2002. MR 1871219 (2002k:30001), DOI 10.1007/978-1-4757-4999-1 – reference: Dieter Gaier, The Faber operator and its boundedness, J. Approx. Theory 101 (1999), no. 2, 265–277. MR 1726457 (2000i:41028), DOI 10.1006/jath.1999.3400 – reference: E. B. Saff and N. Stylianopoulos, On the zeros of asymptotically extremal polynomial sequences in the plane, J. Approx. Theory 191 (2015), 118–127. MR 3306314, DOI 10.1016/j.jat.2014.10.003 – reference: G. Szegö, Über einen Satz von A. Markoff, Math. Z. 23 (1925), no. 1, 45–61 (German). MR 1544730, DOI 10.1007/BF01506220 – reference: F. G. Abdullaev, On some properties of polynomials, orthogonal with respect to area, in domains of the complex plane. I, Ukraïn. Mat. Zh. 52 (2000), no. 12, 1587–1595 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 52 (2000), no. 12, 1807–1817 (2001). MR 1834619 (2002c:30005), DOI 10.1023/A:1010491406926 – reference: R. Sherman Lehman, Development of the mapping function at an analytic corner, Pacific J. Math. 7 (1957), 1437–1449. MR 0095259 (20 \#1765) – reference: Ch. Pommerenke, Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 299, Springer-Verlag, Berlin, 1992. MR 1217706 (95b:30008), DOI 10.1007/978-3-662-02770-7 – reference: A. C. Schaeffer and G. Szegö, Polynomials whose real part is bounded on a given curve in the complex plane, Amer. J. Math. 62 (1940), 868–876. MR 0002604 (2,83a) – reference: Vilmos Totik, Christoffel functions on curves and domains, Trans. Amer. Math. Soc. 362 (2010), no. 4, 2053–2087. MR 2574887 (2011b:30006), DOI 10.1090/S0002-9947-09-05059-4 – reference: Igor E. Pritsker, Derivatives of Faber polynomials and Markov inequalities, J. Approx. Theory 118 (2002), no. 2, 163–174. MR 1932572 (2003g:30007), DOI 10.1006/jath.2002.3713 – reference: V. V. Andrievskii, V. I. Belyi, and V. K. Dzjadyk, Conformal invariants in constructive theory of functions of complex variable, Advanced Series in Mathematical Science and Engineering, vol. 1, World Federation Publishers Company, Atlanta, GA, 1995. Translated from the Russian by D. N. Kravchuk. MR 1421773 (98j:30041) – reference: Dieter Gaier, On a polynomial lemma of Andrievskiĭ, Arch. Math. (Basel) 49 (1987), no. 2, 119–123. MR 901822 (89d:30005), DOI 10.1007/BF01200474 – reference: V. I. Belyĭ, Conformal mappings and approximation of analytic functions in domains with quasiconformal boundary, Mat. Sb. (N.S.) 102(144) (1977), no. 3, 331–361 (Russian). MR 0460648 (57 \#641) – reference: P. K. Suetin, Polynomials orthogonal over a region and Bieberbach polynomials, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by R. P. Boas. MR 0463793 (57 \#3732b) – reference: Nikos Stylianopoulos, Strong asymptotics for Bergman polynomials over domains with corners and applications, Constr. Approx. 38 (2013), no. 1, 59–100. MR 3078274, DOI 10.1007/s00365-012-9174-y – reference: Igor E. Pritsker, Comparing norms of polynomials in one and several variables, J. Math. Anal. Appl. 216 (1997), no. 2, 685–695. MR 1489606 (98j:30002), DOI 10.1006/jmaa.1997.5699 |
| SSID | ssj0000402451 ssj0001648940 ssib056838744 |
| Score | 1.8141421 |
| Snippet | Let
The asymptotic behaviour
of |
| SourceID | proquest ams |
| SourceType | Publisher |
| StartPage | 187 |
| Title | Boundary Estimates for Bergman Polynomials in Domains with Corners |
| URI | https://www.ams.org/conm/661/13282/ http://ebookcentral.proquest.com/lib/SITE_ID/reader.action?docID=4901790&ppg=198 |
| Volume | 661 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1La9tAEF4c99L20idN-kCF3lLZkvch6dCLU5tQSOghgdzE7mpVCrEUbKfg_Mb8qM7srtZy40NbMLIQ-0A7387MjuZByCepU6kZ17GoJzRmSlex5MbEiaIg72StlTXon52L00v27YpfDQb3Pa-l27Ua6bu9cSX_Q1V4BnTFKNl_oGwYFB7APdAXrkBhuP6h_O6aWV2FIVfFbOvUirU3XTbYX-Z4DvLKkjYE33v33Q3aNdqb9vbaOdidj_qomdoqS8vN8Qy2_gL1UOuHODXLH2js_95ebzCOGXMuw4xf24VEFxtrzD1pl413p7dvb1ZfdlJfnYUEsTumhlR0sXcdOMI3pNABM5a0IWVJOJemLENmQF0mJs_OJhmcVlNvzTSO3WI2UxChWZ8fC5ed3XPU1MtjJ5xTV7L6Ad9PCnSU1G0Dm2gOA6A9gk7yyVbKdV_2bdAVkBFawA-9eOVihS4je_t3_6Obqt4dK5ygYOoSO5bQrbSND8hBlrMheQSaxSzYjrjIaag1YPUEhp-9061FULC8YM4o6JfKRiL6paRdgrJuaUMK0mSM849h_rGd3yYNXj1QLqzGdPGMPMUomgjDW-BVnpOBaV6QJz0MvCTTDmxRAFsEYIs82KIe2KKfTeTBFiHYIg-2V-RyPrs4OY19SY9Yguq-jqXgCuRvkRhKc6nhMKKpzOuqgoNJRVMh68JwUbE0VUwIWfAaFHBoDnqkqjlX9DUZNm1j3pCI8gp4idCGm4JVKld1xVmdGw0jsYJWh-QjrEJpfQ5W5X5KHZLP3Rq5ht4jWrvFWZWsQImVlBktAXpHfzHkW_J4u3XekSHse_Me9Na1-uAB8Rt274-0 |
| linkProvider | ProQuest Ebooks |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.title=Modern+Trends+in+Constructive+Function+Theory&rft.au=Stylianopoulos%2C+N.&rft.atitle=Boundary+Estimates+for+Bergman+Polynomials+in+Domains+with+Corners&rft.series=Contemporary+Mathematics&rft.date=2016-03-31&rft.pub=American+Mathematical+Society&rft.isbn=9781470425340&rft.issn=0271-4132&rft.eissn=1098-3627&rft.volume=661&rft.spage=187&rft.epage=198&rft_id=info:doi/10.1090%2Fconm%2F661%2F13282&rft.externalDBID=https%3A%2F%2Fwww.ams.org%2Fconm%2F661%2F13282%2F13282.pdf&rft.externalDocID=10_1090_conm_661_13282 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Febookcentral.proquest.com%2Fcovers%2F4901790-l.jpg |