Orthogonal Dirichlet polynomials with arctangent density

@article{Lubinsky2014OrthogonalDP,
  title={Orthogonal Dirichlet polynomials with arctangent density},
  author={Doron S. Lubinsky},
  journal={Journal of Approximation Theory},
  year={2014},
  volume={177},
  pages={43-56}
}
Let {λj}∞j=1 be a strictly increasing sequence of positive numbers with λ1 = 1. We find a simple explicit formula for the orthogonal Dirchlet polynomials {φn} formed from linear combinations of { λ j n j=1 , associated with the arctangent density. Thus ∫ ∞ −∞ φn (t)φm (t) dt π (1 + t2) = δmn. We obtain formulae for their Christoffel functions, and deduce their asymptotics, as well as universality limits, and spacing of zeros for their reproducing kernels. We also investigate the relationship… CONTINUE READING

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