Abstract:We consider biorthogonal systems of functions associated to derivatives of orthogonal polynomials in the case of general weights. For Freud polynomials, it is proved that the derivatives of any orders of them constitute Hilbertian bases in the space of weighted square integrable functions. §1. IntroductionIt is known a characteristic property of the classical orthogonal polynomials, which states that their derivatives are also orthogonal polynomials. Such a property has many applications in the theory of ortho… Show more
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