Affiliation:
1. School of Mathematical Sciences, NISER Bhubaneswar, India
Abstract
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.
Publisher
National Library of Serbia
Reference34 articles.
1. M. Alfaro and L. Moral, Quasi-orthogonality on the unit circle and semi-classical forms, Portugal. Math. 51 (1994), no. 1, 47-62.
2. G. E. Andrews, R. Askey and R. Roy, Special functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge Univ. Press, Cambridge, 1999.
3. K. K. Behera and A. Swaminathan, Biorthogonality and para-orthogonality of RI polynomials, Calcolo 55 (2018), no. 4, Art. 41, 22 pp.
4. C. F. Bracciali, F. Marcellán and S. Varma Orthogonality of quasi-orthogonal polynomials, Filomat 32(20) (2018), 6953-6977.
5. A. Branquinho and F. Marcellán, Generating new classes of orthogonal polynomials, Internat. J. Math. Math. Sci. 19 (1996), no. 4, 643-656.