Ratio Asymptotics for Multiple Orthogonal Polynomials
We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the recurrence coefficients in the nearest neighbor recurrence relations converge.
Saved in:
| Published in | Modern Trends in Constructive Function Theory Vol. 661; pp. 73 - 85 |
|---|---|
| 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/661/13275 |
Cover
| Abstract | We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the
recurrence coefficients in the nearest neighbor recurrence relations converge. |
|---|---|
| AbstractList | We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the
recurrence coefficients in the nearest neighbor recurrence relations converge. |
| Author | Van Assche, Walter |
| Author_xml | – sequence: 1 givenname: Walter surname: Van Assche fullname: Van Assche, Walter email: walter@wis.kuleuven.be organization: Department of Mathematics, KU Leuven, Celestijnenlaan 200 B box 2400, BE-3001 Leuven, Belgium |
| BookMark | eNotkDtPwzAUhQ0URFq6MmdkCfX7MVaIl1RUhGC2HMemgSQOsTv035MS7nKGe74zfHMw60LnALhG8BZBBVc2dO2Kc7RCBAt2ApZKSEQFpFgRKk9BNrZkQTgWZ2A-PRihZAYyiAUq6IhdgEwpIjhGUl6CZYxfcDwKMWUoA-zNpDrk63ho-xRSbWPuw5C_7JtU943Lt0Pahc_QmSZ_Dc2hC21tmngFzv0YbvmfC_DxcP9-91Rsto_Pd-tNYTBBqWDSQS6kkwgJqrxyvioZ8cbgyivIqGWQOFLaEhnMDZfKUl95yysqEBHWkwXA024_hJ-9i0m7MoRv67o0mMbuTJ_cEDVVEAkFNVZa0hG6mSDTxqkfNYL66FMfferRp_7zSX4BDp1j5g |
| ContentType | Book Chapter |
| DBID | FFUUA |
| DEWEY | 511.3/26 |
| DOI | 10.1090/conm/661/13275 |
| 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 | 85 |
| ExternalDocumentID | EBC4901790_29_84 10_1090_conm_661_13275 |
| GroupedDBID | AABBV AAWPO ABARN ABQPQ ACLGV ADVEM AERYV AFOJC AHWGJ AJFER ALMA_UNASSIGNED_HOLDINGS AZZ BBABE CZZ GEOUK S5T FFUUA |
| ID | FETCH-LOGICAL-a231t-58e0678e811749f9efdb53faa2df9054c503e3bcb1a26a689c4fdfc6d47137cf3 |
| 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-a231t-58e0678e811749f9efdb53faa2df9054c503e3bcb1a26a689c4fdfc6d47137cf3 |
| OCLC | 993762188 |
| PQID | EBC4901790_29_84 |
| PageCount | 13 |
| ParticipantIDs | proquest_ebookcentralchapters_4901790_29_84 ams_ebooks_10_1090_conm_661_13275 |
| 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 | A. I. Aptekarev, V. A. Kalyagin, and E. B. Saff, Higher-order three-term recurrences and asymptotics of multiple orthogonal polynomials, Constr. Approx. 30 (2009), no. 2, 175–223. MR 2519660 (2010h:42049), DOI 10.1007/s00365-008-9032-0 Evi Daems, Arno B. J. Kuijlaars, and Willem Veys, Asymptotics of non-intersecting Brownian motions and a 4×44\times 4 Riemann-Hilbert problem, J. Approx. Theory 153 (2008), no. 2, 225–256. MR 2450071 (2009k:60180), DOI 10.1016/j.jat.2007.10.003 Maciej Haneczok and Walter Van Assche, Interlacing properties of zeros of multiple orthogonal polynomials, J. Math. Anal. Appl. 389 (2012), no. 1, 429–438. MR 2876509 (2012k:42054), DOI 10.1016/j.jmaa.2011.11.077 Mourad E. H. Ismail, Classical and quantum orthogonal polynomials in one variable, Encyclopedia of Mathematics and its Applications, vol. 98, Cambridge University Press, Cambridge, 2005. With two chapters by Walter Van Assche; With a foreword by Richard A. Askey. MR 2191786 (2007f:33001), DOI 10.1017/CBO9781107325982 A. I. Aptekarev, V. Kalyagin, G. López Lagomasino, and I. A. Rocha, On the limit behavior of recurrence coefficients for multiple orthogonal polynomials, J. Approx. Theory 139 (2006), no. 1-2, 346–370. MR 2220045 (2007a:42048), DOI 10.1016/j.jat.2005.09.011 Alexander I. Aptekarev, Pavel M. Bleher, and Arno B. J. Kuijlaars, Large nn limit of Gaussian random matrices with external source. II, Comm. Math. Phys. 259 (2005), no. 2, 367–389. MR 2172687 (2006f:82036), DOI 10.1007/s00220-005-1367-9 E. Daems and A. B. J. Kuijlaars, Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions, J. Approx. Theory 146 (2007), no. 1, 91–114. MR 2327475 (2008g:60245), DOI 10.1016/j.jat.2006.12.001 François Ndayiragije and Walter Van Assche, Asymptotics for the ratio and the zeros of multiple Charlier polynomials, J. Approx. Theory 164 (2012), no. 6, 823–840. MR 2914738, MR 3044041, DOI 10.1016/j.jat.2012.03.005 V. A. Kaliaguine, On operators associated with Angelesco systems, East J. Approx. 1 (1995), no. 2, 157–170. MR 1391763 (97c:41018) Walter Van Assche, Jeffrey S. Geronimo, and Arno B. J. Kuijlaars, Riemann-Hilbert problems for multiple orthogonal polynomials, Special functions 2000: current perspective and future directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., vol. 30, Kluwer Acad. Publ., Dordrecht, 2001, pp. 23–59. MR 2006283 (2004e:30065), DOI 10.1007/978-94-010-0818-1_2 P. M. Bleher and A. B. J. Kuijlaars, Random matrices with external source and multiple orthogonal polynomials, Int. Math. Res. Not. 3 (2004), 109–129. MR 2038771 (2004k:82034), DOI 10.1155/S1073792804132194 A. I. Aptekarev, G. Lopes Lagomasino, and I. A. Rocha, Asymptotic behavior of the ratio of Hermite-Padé polynomials for Nikishin systems, Mat. Sb. 196 (2005), no. 8, 3–20 (Russian, with Russian summary); English transl., Sb. Math. 196 (2005), no. 7-8, 1089–1107. For original Russian: DOI 10.4213/sm1404; for English translation: DOI 10.1070/SM2005v196n08ABEH002329. MR 2188362 (2006h:41040) Pavel Bleher and Arno B. J. Kuijlaars, Large nn limit of Gaussian random matrices with external source. I, Comm. Math. Phys. 252 (2004), no. 1-3, 43–76. MR 2103904 (2005i:82031), DOI 10.1007/s00220-004-1196-2 Peter Henrici, Applied and computational complex analysis. Vol. 2, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1991. Special functions—integral transforms—asymptotics—continued fractions; Reprint of the 1977 original; A Wiley-Interscience Publication. MR 1164865 (93b:30001) S. Delvaux, A. López, and G. López Lagomasino, On a family of Nikishin systems with periodic recurrence coefficients, Mat. Sb. 204 (2013), no. 1, 47–78 (Russian, with Russian summary); English transl., Sb. Math. 204 (2013), no. 1-2, 43–74. For original Russian: DOI 10.4213/sm8076; for English translation: DOI 10.1070/SM2013v204n01ABEH004291. MR 3060076 Pavel M. Bleher and Arno B. J. Kuijlaars, Large nn limit of Gaussian random matrices with external source. III. Double scaling limit, Comm. Math. Phys. 270 (2007), no. 2, 481–517. MR 2276453 (2008b:82032), DOI 10.1007/s00220-006-0159-1 Walter Van Assche, Nearest neighbor recurrence relations for multiple orthogonal polynomials, J. Approx. Theory 163 (2011), no. 10, 1427–1448. MR 2832734 (2012h:42052), DOI 10.1016/j.jat.2011.05.003 Abey López García and Guillermo López Lagomasino, Ratio asymptotic of Hermite-Padé orthogonal polynomials for Nikishin systems. II, Adv. Math. 218 (2008), no. 4, 1081–1106. MR 2419380 (2009e:42053), DOI 10.1016/j.aim.2008.02.007 |
| References_xml | – reference: Walter Van Assche, Nearest neighbor recurrence relations for multiple orthogonal polynomials, J. Approx. Theory 163 (2011), no. 10, 1427–1448. MR 2832734 (2012h:42052), DOI 10.1016/j.jat.2011.05.003 – reference: A. I. Aptekarev, V. Kalyagin, G. López Lagomasino, and I. A. Rocha, On the limit behavior of recurrence coefficients for multiple orthogonal polynomials, J. Approx. Theory 139 (2006), no. 1-2, 346–370. MR 2220045 (2007a:42048), DOI 10.1016/j.jat.2005.09.011 – reference: Walter Van Assche, Jeffrey S. Geronimo, and Arno B. J. Kuijlaars, Riemann-Hilbert problems for multiple orthogonal polynomials, Special functions 2000: current perspective and future directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., vol. 30, Kluwer Acad. Publ., Dordrecht, 2001, pp. 23–59. MR 2006283 (2004e:30065), DOI 10.1007/978-94-010-0818-1_2 – reference: P. M. Bleher and A. B. J. Kuijlaars, Random matrices with external source and multiple orthogonal polynomials, Int. Math. Res. Not. 3 (2004), 109–129. MR 2038771 (2004k:82034), DOI 10.1155/S1073792804132194 – reference: Maciej Haneczok and Walter Van Assche, Interlacing properties of zeros of multiple orthogonal polynomials, J. Math. Anal. Appl. 389 (2012), no. 1, 429–438. MR 2876509 (2012k:42054), DOI 10.1016/j.jmaa.2011.11.077 – reference: A. I. Aptekarev, G. Lopes Lagomasino, and I. A. Rocha, Asymptotic behavior of the ratio of Hermite-Padé polynomials for Nikishin systems, Mat. Sb. 196 (2005), no. 8, 3–20 (Russian, with Russian summary); English transl., Sb. Math. 196 (2005), no. 7-8, 1089–1107. For original Russian: DOI 10.4213/sm1404; for English translation: DOI 10.1070/SM2005v196n08ABEH002329. MR 2188362 (2006h:41040) – reference: E. Daems and A. B. J. Kuijlaars, Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions, J. Approx. Theory 146 (2007), no. 1, 91–114. MR 2327475 (2008g:60245), DOI 10.1016/j.jat.2006.12.001 – reference: V. A. Kaliaguine, On operators associated with Angelesco systems, East J. Approx. 1 (1995), no. 2, 157–170. MR 1391763 (97c:41018) – reference: Peter Henrici, Applied and computational complex analysis. Vol. 2, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1991. Special functions—integral transforms—asymptotics—continued fractions; Reprint of the 1977 original; A Wiley-Interscience Publication. MR 1164865 (93b:30001) – reference: S. Delvaux, A. López, and G. López Lagomasino, On a family of Nikishin systems with periodic recurrence coefficients, Mat. Sb. 204 (2013), no. 1, 47–78 (Russian, with Russian summary); English transl., Sb. Math. 204 (2013), no. 1-2, 43–74. For original Russian: DOI 10.4213/sm8076; for English translation: DOI 10.1070/SM2013v204n01ABEH004291. MR 3060076 – reference: A. I. Aptekarev, V. A. Kalyagin, and E. B. Saff, Higher-order three-term recurrences and asymptotics of multiple orthogonal polynomials, Constr. Approx. 30 (2009), no. 2, 175–223. MR 2519660 (2010h:42049), DOI 10.1007/s00365-008-9032-0 – reference: Evi Daems, Arno B. J. Kuijlaars, and Willem Veys, Asymptotics of non-intersecting Brownian motions and a 4×44\times 4 Riemann-Hilbert problem, J. Approx. Theory 153 (2008), no. 2, 225–256. MR 2450071 (2009k:60180), DOI 10.1016/j.jat.2007.10.003 – reference: Abey López García and Guillermo López Lagomasino, Ratio asymptotic of Hermite-Padé orthogonal polynomials for Nikishin systems. II, Adv. Math. 218 (2008), no. 4, 1081–1106. MR 2419380 (2009e:42053), DOI 10.1016/j.aim.2008.02.007 – reference: Mourad E. H. Ismail, Classical and quantum orthogonal polynomials in one variable, Encyclopedia of Mathematics and its Applications, vol. 98, Cambridge University Press, Cambridge, 2005. With two chapters by Walter Van Assche; With a foreword by Richard A. Askey. MR 2191786 (2007f:33001), DOI 10.1017/CBO9781107325982 – reference: Pavel M. Bleher and Arno B. J. Kuijlaars, Large nn limit of Gaussian random matrices with external source. III. Double scaling limit, Comm. Math. Phys. 270 (2007), no. 2, 481–517. MR 2276453 (2008b:82032), DOI 10.1007/s00220-006-0159-1 – reference: Pavel Bleher and Arno B. J. Kuijlaars, Large nn limit of Gaussian random matrices with external source. I, Comm. Math. Phys. 252 (2004), no. 1-3, 43–76. MR 2103904 (2005i:82031), DOI 10.1007/s00220-004-1196-2 – reference: Alexander I. Aptekarev, Pavel M. Bleher, and Arno B. J. Kuijlaars, Large nn limit of Gaussian random matrices with external source. II, Comm. Math. Phys. 259 (2005), no. 2, 367–389. MR 2172687 (2006f:82036), DOI 10.1007/s00220-005-1367-9 – reference: François Ndayiragije and Walter Van Assche, Asymptotics for the ratio and the zeros of multiple Charlier polynomials, J. Approx. Theory 164 (2012), no. 6, 823–840. MR 2914738, MR 3044041, DOI 10.1016/j.jat.2012.03.005 |
| SSID | ssj0000402451 ssj0001648940 ssib056838744 |
| Score | 1.8484035 |
| Snippet | We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the
recurrence coefficients in the... |
| SourceID | proquest ams |
| SourceType | Publisher |
| StartPage | 73 |
| Title | Ratio Asymptotics for Multiple Orthogonal Polynomials |
| URI | https://www.ams.org/conm/661/13275/ http://ebookcentral.proquest.com/lib/SITE_ID/reader.action?docID=4901790&ppg=84 |
| Volume | 661 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dT9swELegewFexjYE7EOZxBvK6saOY7-ualUhwRACCe0lchwbENAgGiGxv353dpO0hRd4saLIsS7388flcvc7Qg7kwFqkfYtLkfCYC1bGOuUuhsM81ZkrtfSUQscnYnLBjy7Ty670nc8uqYtf5t-reSXvQRXuAa6YJfsGZNtB4QZcA77QAsLQrhi_y27WUGEoVDHrglqx9mZgg32yh2M4rzy0bfJ9cKTc3OupvQ2o4tr-uzhnzhAmQOz5_qGuPH8zBiEeNzGHfx7r6-rKuw5Pq7tnTGjWd0t-g8Gq36D7IdTSwyL9SNXyj7QfmQOe4cpmgVap2TVF4FB_sQNThSGL8C0P03kMndAzwJJQHWWZ7jqUhlthux79HnKFuwTNE5VLvk7WM8l75AOc0qPWD5MKyVrefu9NE1wqTn3m3lxa1hB6NdK3lJ20j-L1Qbi-F82T7M5eHMbewjj_SLYw6yTCdBAQdJus2eknstlpbfaZpB6eaAGeCOCJGniiDp5oAZ4v5GI8Oh9O4nnVi1iDrV3HqbRoQVjMAObKKevKImVO66R0Cgxsk1JmWWGKgU6EFlIZ7kpnRAlmBsuMYzukN62mdpdE1masgActp5IraQpracmFMQKGERndIz_hxXP_W36Wh3AEmqNyclBO7pWzRw4btYSO86BhE_Qxy5fg2n9T769ko5uZ30gP1oj9DjZeXfyYA_4fJIZQBw |
| 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=Simanek%2C+Brian+Z&rft.atitle=Ratio+Asymptotics+for+Multiple+Orthogonal+Polynomials&rft.date=2016-01-01&rft.pub=American+Mathematical+Society&rft.isbn=9781470425340&rft.volume=661&rft_id=info:doi/10.1090%2Fconm%2F661%2F13275&rft.externalDBID=84&rft.externalDocID=EBC4901790_29_84 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Febookcentral.proquest.com%2Fcovers%2F4901790-l.jpg |