On orthogonal polynomials of Sobolev type: algebraic properties and zeros
SIAM Journal on Mathematical Analysis
A generalization of Favad's theorem for polynomials satisfying a recurrence relation
Journal of Approximation Theory
Zero location and nth asymptotics of Sobolev orthogonal polynomials
Journal of Approximation Theory
Sobolev orthogonal polynomial in the complex plane
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
The multiplication operator in Sobolev spaces with respect to measures
Journal of Approximation Theory
Zero location for nonstandard orthogonal polynomials
Journal of Approximation Theory
On a class of Sobolev scalar products in the polynomials
Journal of Approximation Theory
A simple characterization of weighted Sobolev spaces with bounded multiplication operator
Journal of Approximation Theory
Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms
Journal of Approximation Theory
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Sobolev orthogonal polynomials with respect to measures supported on subsets of the complex plane are considered. The connection between the following properties is studied: the multiplication operator Mp(z) = zp(z) defined on the space P of algebraic polynomials with complex coefficients is bounded with respect to the norm defined by the Sobolev inner product, the supports of the measures are compact and the zeros of the orthogonal polynomials lie in a compact subset of the complex plane. In particular, we prove that the boundedness of the multiplication operator M always implies the compactness of the supports.