Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Lebesgue Sobolev orthogonality on the unit circle
Journal of Computational and Applied Mathematics
| Hi-index | 7.30 |
We study the orthogonal polynomials with respect to a Sobolev inner product of the following type: 〈f,g〉s = ∫02π f(eiθ)g(eiθ)|Bh(eiθ)|2 dθ/2π + 1/λ ∫02π f'(eiθg'(eiθ)dθ/2π, 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.The asymptotic 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.