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The Legendre-Type Polynomials and the Laguerre-Type Polynomials in a Sobolev Space

  • Allan M. Krall
Part of the Operator Theory: Advances and Applications book series (OT, volume 133)

Abstract

We give only the highlights of these examples. That the polynomials are orthogonal is relatively easy, but showing that the differential operators, when restricted, remain self-adjoint is more difficult. We refer the interested reader to [3] and [4], for the details, which are quite complicated.

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References

  1. [1]
    W. N. Everitt, A. M. Krall and L. L. Littlejohn, On some properties of the Legendre-type differential expression, Quaes. Math. 13 (1990), 83–108.MathSciNetzbMATHCrossRefGoogle Scholar
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    A. M. Krall, W. N. Everitt and L. L. Littlejohn, The Legendre-type operator in a left definite Hilbert space, Quaes. Math. 15 (1992), 467–475.MathSciNetzbMATHCrossRefGoogle Scholar
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    L. L. Littlejohn and R. Wellman, Left-definite spectral theory with applications to differential operators, manuscript.Google Scholar
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    L. L. Littlejohn, J. Arvesu and F. Marcellan, On the right-definite and left-definite spectral theory of the Legendre polynomials, manuscript.Google Scholar

Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Allan M. Krall
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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