ортогональные по Соболеву

Polynomials Orthogonal with Respect to Sobolev Type Inner Product Generated by Charlier Polynomials

Authors: Sharapudinov I. I., Guseinov I. G.

The problem of constructing of the Sobol ev orthogonal polynomials sαr,n(x) generated by Char li er polynomialssαn(x) is considered. It is shown that the system of polynomials sαr,n(x) generated by Charlier polynomialsis complete in the space Wrl, consisted of the discrete functions, given on the grid Ω = {0, 1, . . .}. Wrlρisa H ilb ert space with the inner product hf, gi. An explicit formula in the form of sαr,k+r(x) =kPl=0brlx[l+r],where xm]= x(x −1) . . . (x − m + 1), is found.

The Fourier Series of the Meixner Polynomials Orthogonal with Respect to the Sobolev-type Inner Product

Authors: Gadzhimirzaev R. M.

In this paper we consider the system of discrete functions {ϕr,k(x)} ∞ k=0 , which is orthonormal with respect to the Sobolev-type inner product hf, gi = Xr−1 ν=0 ∆ ν f(−r)∆ν g(−r) + X t∈Ωr ∆ r f(t)∆r g(t)µ(t), where µ(t) = q t (1−q), 0 < q < 1. It is shown that the shifted classical Meixner polynomials © M−r k (x + r) ª∞ k=r together with functions n (x+r) [k] k! or−1 k=0 form a complete orthogonal system in the space l2,µ(Ωr) with respect to the Sobolev-type inner product.

Sobolev Orthogonal Polynomials Generated by Meixner Polynomials

Authors: Sharapudinov I. I., Gadzhieva Z. D.

The problem of constructing Sobolev orthogonal polynomials mα r,n(x, q) (n = 0, 1, . . .), generated by classical Meixner’s polynomials is considered.