Continuous symmetrized Sobolev inner products of order N (I)
نویسندگان
چکیده
Given a symmetric Sobolev inner product of order N , the corresponding sequence of monic orthogonal polynomials {Qn} satisfies that Q2n(x) = Pn(x), Q2n+1(x) = xRn(x) 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.
منابع مشابه
Continuous Symmetrized Sobolev Inner Products of Order N (ii)
Abstract. Given a symmetrized Sobolev inner product of order N , the corresponding sequence of monic orthogonal polynomials {Qn} satisfies Q2n(x) = Pn(x), Q2n+1(x) = xRn(x) for certain sequences of monic polynomials {Pn} and {Rn}. In this paper we consider the particular case when all the measures that define the symmetrized Sobolev inner product are equal, absolutely continuous and semiclassic...
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