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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 133))

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Abstract

Our goal in the near future is to find and catagorize those boundary value problems which have orthogonal polynomial solutions, but first we must define what we mean by “orthogonal polynomials,” and in order to do so we need some concepts from the theory of distributions.

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References

  1. H. Bremermann, Distributions, Complex Variables and Fourier Transforms, Addison-Wesley, Reading, Mass., 1965.

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  2. I. M. Gelfand and G. E. Shilov, Generalized Functions 1, Academic Press, New York, 1964.

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  3. A. M. Krall, Applied Analysis, D. Reidel, Dordrecht, Netherlands, 1987.

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  4. R. D. Morton and A. M. Krall, Distributional weight functions and orthogonal polynomials, SIAM J. Math. Anal. 9 (1978), 604–626.

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  6. I. Stakgold, Boundary Value Problems of Mathematical Physics, vol. II, Macmillan, New York, 1965.

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© 2002 Springer Basel AG

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Krall, A.M. (2002). Distributions. In: Hilbert Space, Boundary Value Problems and Orthogonal Polynomials. Operator Theory: Advances and Applications, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8155-5_12

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  • DOI: https://doi.org/10.1007/978-3-0348-8155-5_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9459-3

  • Online ISBN: 978-3-0348-8155-5

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