Title of article :
Differential properties for a class of Sobolev orthogonal polynomials
Author/Authors :
Berriochoa، نويسنده , , E. and Cachafeiro، نويسنده , , A.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2002
Abstract :
We study the orthogonal polynomials with respect to a Sobolev inner product of the following type:〈f,g〉s=∫02πf(eiθ)g(eiθ)|Bh(eiθ)|2 dθ2π+1λ∫02πf′(eiθ)g′(eiθ) dθ2π, z=eiθ,where Bh(z) is a complex polynomial of degree h, dθ/2π is the normalized Lebesgue measure and λ is a positive real number.
ymptotic behavior in the complex plane, as well as the differential equations satisfied by the orthogonal polynomials are obtained. As an application, two differential problems are solved, one of them is like a Dirichlet boundary value problem.
Keywords :
orthogonal polynomials , Minimal norm , Recurrence relation , Asymptotics , differential equation
Journal title :
Journal of Computational and Applied Mathematics
Journal title :
Journal of Computational and Applied Mathematics