4 papers · 1 filter
An operator approach to multipoint Pade approximations
Maxim S. Derevyagin, Alexei S. Zhedanov
First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-ste…
Elliptic polynomials orthogonal on the unit circle with a dense point spectrum
Alexei Zhedanov
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We fin…
Generalized Bochner theorem: characterization of the Askey-Wilson polynomials
Luc Vinet, Alexei Zhedanov
Assume that there is a set of monic polynomials satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = λ_n P_n(z(s)), n=…
Biorthogonality of the Lagrange interpolants
Alexei Zhedanov
We show that the Lagrange interpolation polynomials are biorthogonal with respect to a set of rational functions whose poles coinicde with interpolation points