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Representation theorems for Tchebycheffian polynomials with boundary conditions and their applications

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Abstract

Representation theorems for Tchebycheff polynomials with homogeneous boundary conditions are proved, and a number of extremal problems are solved.

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References

  1. F. R. Gantmacher and M. G. Krein,Oscillatory Matrices and Kernels and Small Vibrations of Mechanical Systems, (in Russian), 2nd ed., Moscow, 1950.

  2. S. Karlin,Representation theorems for positive functions, J. Math. Mech.12 (1963), 559–618.

    MathSciNet  Google Scholar 

  3. S. Karlin,Generalized Bernstein inequalities, Acta Sci. Math. (Szeged), (1966), pp. 1–15.

  4. S. Karlin,Total Positivity, Stanford Univ. Press, Stanford, Calif., 1968.

    MATH  Google Scholar 

  5. S. Karlin,Total positivity, interpolation by splines, and Green’s functions of differential operators, J. Approximation Theory4 (1971), 91–112.

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Karlin and J. Karon,On Hermite-Birkhoff interpolation, J. Approximation Theory6 (1972), 90–115.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Karlin and C. A. Micchelli,The fundamental theorem of algebra for monosplines statisfying boundary conditions, Israel J. Math.11 (1972), 405–451.

    MATH  MathSciNet  Google Scholar 

  8. S. Karlin and L. S. Shapley,Geometry of moment spaces, Mem. Amer. Math. Soc.12 (1953).

  9. S. Karlin and W. Studden,Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966.

    MATH  Google Scholar 

  10. C. A. Micchelli and T. J. Rivlin,Quadrature formulae and Hermite-Birkhoff interpolation, IBM J. Res. Develop., RC 3396, June, 1971.

  11. M. A. Neumark,Lineare Differentialoperatoren, Akademie-Verlag, Berlin, 1960.

    MATH  Google Scholar 

  12. I. J. Schoenberg,On Hermite-Birkhoff interpolation, J. Math. Anal. Appl.16 (1966), 538–543.

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Szegö,Orthogonal Polynomials, Amer. Math. Soc., Vol. XXIII, New York, 1969.

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This work is part of the author’s doctoral thesis under the supervision of Professor S. Karlin.

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Pinkus, A. Representation theorems for Tchebycheffian polynomials with boundary conditions and their applications. Israel J. Math. 17, 11–34 (1974). https://doi.org/10.1007/BF02756821

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  • DOI: https://doi.org/10.1007/BF02756821

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