On the problem of modified moments

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The problem of modified moments is studied. Let (Pn(x))n=0 be an orthogonal polynomial sequence. Given a sequence (dn)n=0 of real numbers, does there exist a bounded nondecreasing function with infinitely many points of increase such that for every n ∈ N0, dn = ∫-∞ Pn(x) dμ(x)? Is there any information about the support of μ? A necessary and sufficient condition for the existence of such a function v is given in terms of the positivity of certain determinants. For certain (Pn(x))n=0 a description of the support of v is established.

Original languageEnglish
Pages (from-to)360-362
Number of pages3
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Mar 1984


  • Moment problems
  • Orthogonal polynomials


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