General Sobolev Orthogonal Polynomials |
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| Authors: | Francisco Marcellán Teresa E Pérez Miguel A Piñar André Ronveaux |
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| Institution: | aUniversidad Carlos III de Madrid, Madrid, Spain;bUniversidad de Granada, Granada, Spain;cFacultés Universitaires N. D. de la Paix, Namur, Belgium |
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| Abstract: | In this paper, we study orthogonal polynomials with respect to the inner product (f, g)S(N) =〈u, fg〉+∑m=1N λm〈u, f(m)g(m) 〉, where λm≥0 form=1,…,N, anduis a semiclassical, positive definite linear functional. For these non-standard orthogonal polynomials, algebraic and differential properties are obtained, as well as their representation in terms of the standard orthogonal polynomials associated withu. |
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