CHARACTERIZATIONS OF ORTHOGONAL POLYNOMIALS SATISFYING DIFFERENTIAL-EQUATIONS

In 1938, H. L. Krall found a necessary and sufficient condition for an orthogonal polynomial set {P(n)(x)}0infinity to satisfy a linear differential equation of the form SIGMA(i=0)N l(i)(x)y(i)(x) = lambda(n)y(x). Here the authors give a new simple proof of Krall's theorem as well as some other characterizations of such orthogonal polynomial sets based on the symmetrizability of the differential operator. In particular it is shown that such orthogonal polynomial sets are characterized by a certain Sobolev-type orthogonality, which generalizes Hahn's charaterization of classical orthogonal polynomials.
Publisher
SIAM PUBLICATIONS
Issue Date
1994-05
Language
ENG
Citation

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v.25, no.3, pp.976 - 990

ISSN
0036-1410
URI
http://hdl.handle.net/10203/57369
Appears in Collection
MA-Journal Papers(저널논문)
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