On the positivity of some bilinear functionals in Sobolev spaces
Let \(c^{(m)}\) define a positive definite inner product and \(a(f,g)=\sum_{m=0}^N\lambda_mc^{(m)}(f^{(m)},g^{(m)})\) a bilinear functional. The authors study the domain of \(\{\lambda_m\}\) leading to the positivity of \(a(p,p)\), where \(p\) are polynomials of degree \(n\). The cases of Hermite, Laguerre, Gegenbauer and Jacobi are analysed with help of symbolic computations with Mathematica. For \(N=1\), the Markov-Bernstein inequalities are given.
scientific article; zbMATH DE number 1326531
scientific article