Classical Sobolev orthogonal polynomials: eigenvalue problem
Ficheros
Identificadores
Compartir
Metadatos
Mostrar el registro completo del ítemFecha
2019-07Resumen
We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)d\mu+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $\mu$ is a classical continuous measure with support on the real line (Jacobi, Laguerre or Hermite). The orthonormal polynomials with respect to this Sobolev inner product are eigenfunctions of a differential operator and obtaining the asymptotic behavior of the corresponding eigenvalues is the principal goal of this paper.
Palabra/s clave
Sobolev orthogonal polynomials
Differential operator
Eigenvalues
Asymptotics