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Continuous symmetrized Sobolev inner products of order N (I)

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URI: https://hdl.handle.net/10016/5946
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.11.052
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2005-06-01
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Elsevier
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Abstract
Given a symmetrized Sobolev inner product of order N, the corresponding sequence of monic orthogonal polynomials {Qn} satisfies that Q_2n(x)=Pn(x2), Q_2n+1(x)=xRn(x2) for certain sequences of monic polynomials {Pn} and {Rn}. In this paper, we deduce the integral representation of the inner products such that {Pn} and {Rn} are the corresponding sequences of orthogonal polynomials. Moreover, we state a relation between both inner products which extends the classical result for symmetric linear functionals.
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14 pages, no figures.-- MSC2000 codes: 42C05
MR#: MR2132890 (2005k:42068)
Zbl#: Zbl 1076.42017
Keywords
Sobolev inner product, Orthogonal polynomials, Symmetrization process
Bibliographic citation
Journal of Mathematical Analysis and Applications, 2005, vol. 306, n. 1, p. 83-96
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