When is the Uvarov transformation positive definite? (Q662888)

The authors analyze conditions on \(m\in C\) for \(U(p,q)\) -- the Uvarov transformation of \(L(p,q)\) -- a positive definite bilinear functional, to be positive definite in the linear space of polynomials of degree less than or equal to \(n\). In particular, it is shown that \(m\) has to lie inside a circle in the complex plane defined by \(|\alpha|>1\), \(n\) and the moments associated with \(L\). An upper bound for the radius of this circle that depends only on \(\alpha\) and \(n\), is also given. This and other conditions on \(m\) are visualized for some examples.