Global properties of zeros for Sobolev-type orthogonal polynomials. (English) Zbl 0792.42012

Pérez, Teresa E.; Piñar, Miguel A.

J. Comput. Appl. Math. 49, No. 1-3, 225-232 (1993).

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

Keywords:

zeros; Sobolev-type orthogonal polynomials; Sobolev spaces; localization; separation

References:

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