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The multiplication operator, zero location and asymptotic for non-diagonal Sobolev norms

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URI: http://hdl.handle.net/10016/6448
ISSN: 0167-8019 (Print)
ISSN: 1572-9036 (Online)
DOI: 10.1007/s10440-009-9541-2
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multiplication_touris_aam_2010_ps.pdf (203.22 KB)
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2010
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Springer
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Abstract
In this paper we are going to study the zero location and asymptotic behavior of extremal polynomials with respect to a generalized non-diagonal Sobolev norm in which the product of the function and its derivative appears. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials. The multiplication operator by the independent variable is the main tool in order to obtain our results.
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14 pages, no figures.-- Online version published Jul 9, 2009.
Article in press.
Keywords
Multiplication operator, Zero location, Asymptotic, Weight, Sobolev orthogonal polynomials, Extremal polynomials, Weighted Sobolev spaces
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Acta Applicandae Mathematicae, 2010, doi: 10.1007/s10440-009-9541-2 (In press)
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