Orthogonal polynomials and rational modifications of lebesgue measure on the unit circle. an inverse problem

Reference

• Branquinho , A. and Marcellán , F . 1996 . Generating new classes of orthogonal polynomials . Inter. J. Math. Math. Sci. , 19 : 643 – 656 .
   Google Scholar
• Cachafeiro , A. and Marcellán , F. 1988 . Orthogonal polynomials and jump modifications In Orthogonal Polynomials and their Applications , Edited by: Alfaro , M. 236 – 240 . Berlin : Springer Verlag . Lecture Notes in Mathematics
   Google Scholar
• Erdelyi , T. , Geronimo , J.S. , Nevai , P. and Zhang , J. 1991 . A simple proof of “Favard's Theorem” on the unit circle . Atti Sem. Mat. Fis. Univ. Modena , 29 : 41 – 46 .
   Google Scholar
• Freud , G. 1971 . Orthogonal Polynomials , Oxford : Pergamon Press .
   Google Scholar
• Garcia-Lázaro , P. and Marcellán , F. 1985 . Christoffel formulas for n-kernals associated to Jordan arcs In Polynómes Orthogonaux et Applications , Edited by: Brezinski , C. Vol. 1171 , 195 – 203 . Berlin : Springer Verlag .
   Google Scholar
• Garcia-Lázaro , P. and Moral , L. “ Quasi orthogonality on Laurent polynomials ” . In In Orthogonal Polynomials and their Applications , Edited by: Brezinski , C. 267 – 270 . J.C.Baltzer . IMACS Annals on Comp, and Appl. Math
   Google Scholar
• Geronimus , Ya.L. 1962 . Polynomials orthogonal on a circle and their applications . Amer.Math. Soc. Transl, Series , 3 ( 1 ) : 1 – 78 .
   Google Scholar
• Godoy , E. and Marcellan , F. 1991 . An analog of the Christoffel formula for polynomial modification of a measure on the unit circle . Boll. Un. Mat. It , 7 ( 5-A ) : 1 – 12 .
   Google Scholar
• Godoy , E. and Marcellan , F. 1993 . Orthogonal polynomials and rational modifications of measures . Canad. J. Math , 45 ( 5 ) : 930 – 943 .
   Web of Science ®Google Scholar
• Ismail , M.E.H. and Ruedemann , R.W. 1992 . Relation between polynomials orthogonal on the unit circle with respect to different weights . J Approx. Th. , 71 : 39 – 60 .
   Google Scholar
• Li , X. and Pan , K. 1994 . Asymptotic behaviour of orthogonal polynomials corresponding to measures with discret part off the unit circle . J Approx. Th , 79 : 54 – 71 .
   Google Scholar
• Marcellán , F. and Maroni , P. 1991 . Orthogonal polynomials on the unit circle and their derivatives . Constr. Approx. , 7 : 341 – 348 .
   Google Scholar
• Marcellán , F. , Peherstorfer , F. and Steinbauer , R. 1996 . Orthogonality properties of linear combinations of orthogonal polynomials . Adv. Comp. Math. , 5 : 281 – 295 .
   Google Scholar
• Marcellán , F. and Tasis , C. 1988 . Sobre cuasi-ortogonalidad en la circunferencia unidad. Aplicaciones . In XII Jornadas Matemdticas Hispano-Lusas (Universidad de Valla-dolid) ,
   Google Scholar
• Mate , A. , Nevai , P. and Totik , V. 1991 . Szegö's extremum problem on the unit circle . Ann. Math. , 134 : 433 – 453 .
   Web of Science ®Google Scholar
• Nevai , P. 1987 . Orthogonal polynomials, measures and recurrences on the unit circle . Trans. Amer. Math. Soc , 300 ( 1 ) : 175 – 189 .
   Web of Science ®Google Scholar
• Peherstorfer , F . 1996 . A special class of polynomials orthogonal on the unit circle includ¬ing the associated polynomials . Constr. Approx. , 12 : 161 – 185 .
   Web of Science ®Google Scholar
• Peherstorfer , F. 1990 . Linear combinations of orthogonal polynomials generating positive quadrature formulas . Math. Comput. , 55 : 231 – 241 .
   Google Scholar
• Szegö , G. 1975 . Orthogonal Polynomials , Providence, Rhode Island : Amer Math Soc Colloq Publ . Fourth Ed
   Google Scholar