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Sobolev inner products and orthogonal polynomials of Sobolev type

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Abstract

This survey paper deals with polynomials which are orthogonal with respect to scalar products of the form ∫ R F T[A]G withF T=[f(x), f(Ⅎ(x),...f (y)(x)], [A] ≡A ji =A ji =A ij =dμ ji (I ji ) where dμ ji is a measure of supportI ij and [A] is positive semi-definite. Basic properties are indicated or proved in particular cases.

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Ronveaux, A. Sobolev inner products and orthogonal polynomials of Sobolev type. Numer Algor 3, 393–399 (1992). https://doi.org/10.1007/BF02141946

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AMS subject classification

  • 33A65

Keywords

  • Orthogonal polynomials
  • Sobolev inner product