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Sobolev orthogonal polynomials and spectral differential equations
1995
Transactions of the American Mathematical Society
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We find necessary and sufficient conditions for a spectral differential equation N LN[y](x) = 52t¡(x)yW(x) = kny(x) (-1 to have Sobolev orthogonal polynomials of solutions, which are orthogonal relative to the Sobolev (pseudo-) inner product c t (P ,q)= / Pqdn + I p'q'du, Jr Jr where d/i and dv are signed Borel measures having finite moments. This result generalizes a result by H. L. Krall, which handles the case when dv = 0 .
doi:10.1090/s0002-9947-1995-1308015-9
fatcat:m53cmkewf5fixpncfrzp42ofeu