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Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product. (English) Zbl 0840.42017
The asymptotic behavior of polynomials orthogonal with respect to the discrete Sobolev inner product $\langle h, g\rangle= \int hg d\mu+ \sum^m_{j= 1} \sum^{N_j}_{i= 1} M_{j, i} h^{(i)}(c_j) g^{(i)} (c_j)$ is investigated. In the definition of the inner product $$\mu$$ is a certain type of real or complex measure defined on the real axis, and the $$c_j$$ are complex numbers in the complement of $$\text{supp}(\mu)$$. The polynomials are called Sobolev orthogonal polynomials. The main group of results deals with relative asymptotics, i.e., the asymptotic behavior $$(n\to \infty)$$ of the quotient $$Q_n/L_n$$, where $$Q_n$$ is the Sobolev orthogonal polynomial of order $$n$$ and $$L_n$$ the polynomial orthogonal with respect to the measure $$\mu$$.
Reviewer: H.Stahl (Berlin)

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