In mathematics, Sobolev orthogonal polynomials are orthogonal polynomials with respect to a Sobolev inner product, i.e. an inner product with derivatives.
By having conditions on the derivatives, the Sobolev orthogonal polynomials in general no longer share some of the nice features that classical orthogonal polynomials have.
be positive Borel measures on
The Sobolev orthogonal polynomials
denotes the Kronecker delta.
One says that these polynomials are sobolev orthogonal.