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Global properties of zeros for Sobolev-type orthogonal polynomials. (English) Zbl 0792.42012
Summary: In this paper we analyze some properties concerning the zeros of orthogonal polynomials $$Q_ n(x)$$, associated to the inner product $\langle f,g\rangle= \int_ I f(x)g(x)d\mu(x)+ Mf(c)g(c)+ Nf'(c)g'(c),$ where $$I$$ is a (not necessarily bounded) real interval, $$\mu$$ is a positive measure on $$I$$, $$c\in\mathbb{R}$$ and $$M$$, $$N\geq 0$$. In particular, some properties concerning the localization and separation for the roots of $$Q_ n(x)$$ are obtained.

MSC:
 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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References:
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