Division problem of moment functionals

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For a quasi-definite moment functional sigma and nonzero polynomials A(x) and D(x), we define another moment functional tau by the relation D(x)tau = A(x)sigma. In other words, tau is obtained from sigma by a linear spectral transform. We find necessary and sufficient conditions for tau to be quasi-definite when D(x) and A(x) have no nontrivial common factor. When tau is also quasi-definite, we also find a simple representation of orthogonal polynomials relative to tau in terms of orthogonal polynomials relative to sigma. We also give two illustrative examples when sigma is the Laguerre or Jacobi moment functional.
Publisher
ROCKY MT MATH CONSORTIUM
Issue Date
2002
Language
English
Article Type
Article; Proceedings Paper
Keywords

ORTHOGONAL POLYNOMIALS

Citation

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, v.32, no.2, pp.739 - 758

ISSN
0035-7596
URI
http://hdl.handle.net/10203/81776
Appears in Collection
MA-Journal Papers(저널논문)
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