Biorthogonality and para-orthogonality of 
                
                  
                
                $$R_I$$
                
                  
                    
                      R
                      I
                    
                  
                
               polynomials

In this paper we study quasi-orthogonality on the unit circle based on the structural and orthogonal properties of a class of self-invariant polynomials. We discuss a special case in which these polynomials are represented in terms of the reversed Szeg? polynomials of consecutive degrees and illustrate the results using contiguous relations of hypergeometric functions. This work is motivated partly by the fact that recently cases have been made to establish para-orthogonal polynomials as the unit circle analogues of quasi-orthogonal polynomials on the real line so far as spectral properties are concerned. We show that structure wise too there is great analogy when self-inversive polynomials are used to study quasi-orthogonality on the unit circle.

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Biorthogonality and para-orthogonality of $$R_I$$ R I polynomials

Cited by 3 publications

References 26 publications

Spectral properties related to generalized complementary Romanovski–Routh polynomials

Spectral properties related to generalized complementary Romanovski–Routh polynomials

Chain sequences and zeros of polynomials related to a perturbed RII type recurrence relation

Self-inversive polynomials and quasi-orthogonality on the unit circle

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