Let L be a positive definite bilinear functional, then the Uvarov transformation of L is given byIn this paper we analyze conditions on m for U to be positive definite in the linear space of polynomials of degree less than or equal to n. In particular, we show that m has to lie inside a circle in the complex plane defined by α, n and the moments associated with L. We also give an upper bound for the radius of this circle that depends only on α and n. This and other conditions on m are visualized for some examples.

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