orthogonal polynomials;
Turan inequalities;
three term recurrence;
D O I:
暂无
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We use Turan type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1=xpk-ckpk-1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Mate, Nevai and Totik result on the largest zeros of orthogonal polynomials with ck=ck(2 delta)(1+o(k(-2/3))).our proof is based on new Turan inequalituies Which are obtained by analogy with higher order laguerre in equalities.
机构:
Univ Estadual Paulista, IBILCE, Dept Ciencias Computacao & Estatist, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilUniv Estadual Paulista, IBILCE, Dept Ciencias Computacao & Estatist, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
Dimitrov, DK
Ronveaux, A
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机构:Univ Estadual Paulista, IBILCE, Dept Ciencias Computacao & Estatist, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
机构:
Univ Sofia, Dept Math & Informat, 5 James Bourchier Blvd, Sofia 1164, BulgariaUniv Sofia, Dept Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria
Nikolov, Geno
Shadrin, Alexei
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机构:
Univ Cambridge, Dept Appl Math & Theoret Phys DAMTP, Wilberforce Rd, Cambridge CB3 0WA, EnglandUniv Sofia, Dept Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria