{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T16:28:40Z","timestamp":1773246520519,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,6,12]],"date-time":"2012-06-12T00:00:00Z","timestamp":1339459200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s11075-012-9594-6","type":"journal-article","created":{"date-parts":[[2012,6,11]],"date-time":"2012-06-11T11:28:39Z","timestamp":1339414119000},"page":"669-681","source":"Crossref","is-referenced-by-count":4,"title":["Zeros of Sobolev orthogonal polynomials on the unit circle"],"prefix":"10.1007","volume":"60","author":[{"given":"K.","family":"Castillo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L. E.","family":"Garza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Marcell\u00e1n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,6,12]]},"reference":[{"key":"9594_CR1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0377-0427(95)00034-8","volume":"69","author":"M Alfaro","year":"1996","unstructured":"Alfaro, M., L\u00f3pez, G., Rezola, M.L.: Some properties of zeros of Sobolev-type orthogonal polynomials. J. Comput. Appl. Math. 69, 171\u2013179 (1996)","journal-title":"J. Comput. Appl. Math."},{"key":"9594_CR2","first-page":"27","volume":"3","author":"GS Ammar","year":"1994","unstructured":"Ammar, G.S., Gragg, W.G.: Schur flows for orthogonal Hessenberg matrices. Fields Inst. Commun. 3, 27\u201334 (1994)","journal-title":"Fields Inst. Commun."},{"key":"9594_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0793-1","volume-title":"Polynomials and polynomials inequalities","author":"P Borwein","year":"1995","unstructured":"Borwein, P., Erd\u00e9lyi, T.: Polynomials and polynomials inequalities. Springer Verlag, New York (1995)"},{"key":"9594_CR4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s00365-001-0005-9","volume":"18","author":"A Branquinho","year":"2002","unstructured":"Branquinho, A., Foulqui\u00e9, A., Marcell\u00e1n, F.: Asymptotic behavior of Sobolev-type orthogonal polynomials on a rectifiable Jordan curve or arc. Constr. Approx. 18, 161\u2013182 (2002)","journal-title":"Constr. Approx."},{"key":"9594_CR5","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1016\/j.aml.2011.11.015","volume":"25","author":"K Castillo","year":"2012","unstructured":"Castillo, K.: A new approach to relative asymptotic behavior to Sobolev-type inner product on the unit circle. Appl. Math. Lett. 25, 1000\u20131004 (2012)","journal-title":"Appl. Math. Lett."},{"key":"9594_CR6","author":"K Castillo","year":"2012","unstructured":"Castillo, K., Garza, L., Marcell\u00e1n, F.: Asymptotic behavior of Sobolev orthogonal polynomials on the unit circle. Integral Transforms Spec. Funct. (2012). doi: 10.1080\/10652469.2011.649751","journal-title":"Integral Transforms Spec. Funct."},{"key":"9594_CR7","author":"K Castillo","year":"2012","unstructured":"Castillo, K., Mello, M.V., Rafaeli, F.R.: Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: a general case. Appl. Numer. Math. (2012). doi: 10.1016\/j.apnum.2012.05.006","journal-title":"Appl. Numer. Math."},{"key":"9594_CR8","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.cam.2006.02.041","volume":"202","author":"L Daruis","year":"2007","unstructured":"Daruis, L., Hern\u00e1ndez, J., Marcell\u00e1n, F.: Spectral transformations for Hermitian Toeplitz matrices. J. Comput. Appl. Math. 202, 155\u2013176 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"9594_CR9","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0168-9274(99)00136-1","volume":"36","author":"L Daruis","year":"1999","unstructured":"Daruis, L., Gonz\u00e1lez-Vera, P.: Szeg\u0151 polynomials and quadrature formulas on the unit circle. Appl. Numer. Math. 36, 79\u2013112 (1999)","journal-title":"Appl. Numer. Math."},{"key":"9594_CR10","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1006\/jath.1999.3357","volume":"100","author":"A Foulqui\u00e9","year":"1999","unstructured":"Foulqui\u00e9, A., Marcell\u00e1n, F., Pan, K.: Asymptotic behavior of Sobolev-type orthogonal polynomials on the unit circle. J. Approx. Theory 100, 345\u2013363 (1999)","journal-title":"J. Approx. Theory"},{"key":"9594_CR11","first-page":"411","volume":"52","author":"A Foulqui\u00e9 Moreno","year":"1998","unstructured":"Foulqui\u00e9 Moreno, A., Marcell\u00e1n, F., Peherstorfer, F., Steinbauer, R.: Strong asymptotics on the support of the measure of orthogonality for polynomials orthogonal with respect to a discrete Sobolev inner product on the unit circle. Rendi. Circ. Matem. Palermo 52, 411\u2013425 (1998)","journal-title":"Rendi. Circ. Matem. Palermo"},{"key":"9594_CR12","volume-title":"Orthogonal polynomials","author":"YL Geronimus","year":"1961","unstructured":"Geronimus, Y.L.: Orthogonal polynomials. Consultants Bureau, New York (1961)"},{"key":"9594_CR13","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1112\/blms\/21.2.113","volume":"21","author":"WB Jones","year":"1989","unstructured":"Jones, W.B., Nj\u00e5stad, O., Thron, W.J.: Moment theory, orthogonal polynomials, quadrature and continued fractions associated with the unit circle. Bull. Lond. Math. Soc. 21, 113\u2013152 (1989)","journal-title":"Bull. Lond. Math. Soc."},{"key":"9594_CR14","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0377-0427(93)90297-O","volume":"46","author":"WB Jones","year":"1993","unstructured":"Jones, W.B., Nj\u00e5stad, O., Thron, W.J., Waadeland, H.: Szeg\u0151 polynomials applied to frequency analysis. J. Comput. Appl. Math. 46, 217\u2013228 (1993)","journal-title":"J. Comput. Appl. Math."},{"key":"9594_CR15","doi-asserted-by":"crossref","first-page":"127","DOI":"10.2140\/pjm.1996.175.127","volume":"175","author":"X Li","year":"1996","unstructured":"Li, X., Marcell\u00e1n, F.: On polynomials orthogonal with respect to a Sobolev inner product on the unit circle. Pacific J. Math. 175, 127\u2013146 (1996)","journal-title":"Pacific J. Math."},{"key":"9594_CR16","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/S0096-3003(01)00079-0","volume":"128","author":"F Marcell\u00e1n","year":"2002","unstructured":"Marcell\u00e1n, F., Moral, L.: Sobolev-type orthogonal polynomials on the unit circle. Appl. Math. Comput. 128, 329\u2013363 (2002)","journal-title":"Appl. Math. Comput."},{"key":"9594_CR17","doi-asserted-by":"crossref","first-page":"3929","DOI":"10.1090\/S0002-9939-2011-10806-2","volume":"139","author":"F Marcell\u00e1n","year":"2011","unstructured":"Marcell\u00e1n, F., Rafaeli, F.R.: Monotonicity and asymptotic of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher derivatives. Proc. Amer. Math. Soc. 139, 3929\u20133936 (2011)","journal-title":"Proc. Amer. Math. Soc."},{"key":"9594_CR18","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/0021-9045(82)90071-5","volume":"36","author":"A Mat\u00e9","year":"1982","unstructured":"Mat\u00e9, A., Nevai, P.: Remarks on E.A. Rahmanov\u2019s paper on the asymptotics of the ratio of orthogonal polynomials. J. Approx. Theory 36, 64\u201372 (1982)","journal-title":"J. Approx. Theory"},{"key":"9594_CR19","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF01890553","volume":"3","author":"A Mat\u00e9","year":"1987","unstructured":"Mat\u00e9, A., Nevai, P., Totik, V.: Extensions of Szeg\u0151\u2019s theory of orthogonal polynomials II. Constr. Approx. 3, 51\u201372 (1987)","journal-title":"Constr. Approx."},{"key":"9594_CR20","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/S0377-0427(01)00388-0","volume":"139","author":"A Mukaihira","year":"2002","unstructured":"Mukaihira, A., Nakamura, Y.: Schur flow for orthogonal polynomials on the unit circle and its integrable discretization. J. Comput. Appl. Math. 139, 75\u201394 (2002)","journal-title":"J. Comput. Appl. Math."},{"key":"9594_CR21","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1006\/jmaa.1997.5233","volume":"206","author":"O Nj\u00e5stad","year":"1997","unstructured":"Nj\u00e5stad, O., Waadeland, H.: Generalized Szeg\u0151 theory in frequency analysis. J. Math. Anal. Appl. 206, 289\u2013307 (1997)","journal-title":"J. Math. Anal. Appl."},{"key":"9594_CR22","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1070\/SM1983v046n01ABEH002749","volume":"53","author":"EA Rakhmanov","year":"1983","unstructured":"Rakhmanov, E.A.: On the asymptotics of the ratio of orthogonal polynomials II. USSR Sbornik, 53, 105\u2013117 (1983)","journal-title":"USSR Sbornik"},{"key":"9594_CR23","unstructured":"Simon, B.: Orthogonal Polynomials on the Unit Circle, 2 vols. Amer. Math. Soc. Coll. Publ. Series, vol. 54. Amer. Math. Soc. Providence, Rhode Island (2005)"},{"key":"9594_CR24","doi-asserted-by":"crossref","first-page":"189","DOI":"10.3934\/ipi.2007.1.189","volume":"1","author":"B Simon","year":"2007","unstructured":"Simon, B.: Zeros of OPUC and long time asymptotics of Schur and related flows. Inverse Probl. Imag. 1, 189\u2013215 (2007)","journal-title":"Inverse Probl. Imag."},{"key":"9594_CR25","unstructured":"Szeg\u0151, G.: Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. Series, 4th edn., vol. 23. Amer. Math. Soc. Providence, Rhode Island (1975)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9594-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-012-9594-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9594-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:18Z","timestamp":1559365698000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-012-9594-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,12]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["9594"],"URL":"https:\/\/doi.org\/10.1007\/s11075-012-9594-6","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,12]]}}}