Noncommutative biorthogonal polynomials

Advances in Applied Mathematics（2012）

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摘要

We define and study biorthogonal sequences of polynomials over noncommutative rings, generalizing previous treatments of biorthogonal polynomials over commutative rings and of orthogonal polynomials over noncommutative rings. We extend known recurrence relations for specific cases of biorthogonal polynomials and prove a general version of Favard@?s theorem.

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关键词

commutative ring,orthogonal polynomial,noncommutative biorthogonal polynomial,noncommutative ring,general version,study biorthogonal sequence,previous treatment,recurrence relation,biorthogonal polynomial,specific case,quantum algebra,recurrence relations

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